MAKE THE PICKLED CARROTS (AT LEAST 1 HOUR AHEAD):
1. Using a vegetable peeler or mandoline, shave the carrot into thin ribbons. Place in a small heatproof bowl or jar.
2. Combine the vinegar, water, sugar, salt and mustard seeds (if using) in a small saucepan. Bring to a boil, stirring until the sugar dissolves.
3. Pour the hot brine over the carrot ribbons and let cool to room temperature, then refrigerate. The pickles will be ready after 1 hour but improve overnight. They will keep refrigerated for up to 2 weeks.

MAKE THE PASTRY:
4. Combine the flour and salt in a bowl (or pulse in a food processor). Add the cold butter and rub in with your fingertips (or pulse) until the mixture resembles fine breadcrumbs with a few pea-sized pieces remaining.
5. Add the egg yolk and 1 tablespoon of ice water. Mix (or pulse) until the dough just begins to clump together, adding the remaining water only if needed. The dough should hold together when pressed but not feel wet or sticky.
6. Flatten into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
7. Preheat the oven to 375°F (190°C).
8. Roll the pastry very thin — no more than 1/8 inch (2-3 mm) thick. This is the single most important step for addressing the 'too much crumb' critique. A thick tart case overwhelms the delicate filling; a thin, crisp shell frames it.
9. Cut out rounds using a 2 1/2-inch (6 cm) cutter and press gently into a 24-hole mini muffin or mini tartlet pan, ensuring the pastry fits snugly without stretching. Prick the bases lightly with a fork.
10. Blind bake for 10-12 minutes until the pastry is light golden and feels dry to the touch. If the bases puff up during baking, gently press them down with the back of a teaspoon as soon as they come out. Let cool slightly in the pan.

MAKE THE CARROT PURÉE:
11. Place the chopped carrots in a saucepan, cover with cold water and add a pinch of salt. Bring to a boil, then simmer for 15-18 minutes until completely tender — they should offer no resistance when pierced with a knife.
12. Drain well. Transfer to a blender or small food processor with the butter, orange juice and cumin. Blend until very smooth and silky. Season with salt to taste. The purée should be thick enough to hold its shape on a spoon. If it is too thin, return to the pan and cook gently for a few minutes to reduce.
13. Transfer to a piping bag fitted with a small round tip, or a squeeze bottle. Set aside.

PREPARE THE SAUTÉED MUSHROOMS:
14. Heat the butter in a skillet over medium-high heat until foaming. Add the diced mushrooms and spread them in a single layer — do not stir for the first minute to allow browning.
15. Add the thyme and garlic, season with salt and pepper, and cook for another 2-3 minutes until the mushrooms are golden and any released liquid has evaporated.
16. Deglaze with the sherry or wine, stirring until it evaporates completely. The mushrooms should be deeply flavored and dry — any residual moisture will make the custard soggy. Set aside to cool slightly.

MAKE THE GRUYÈRE CUSTARD AND ASSEMBLE:
17. Reduce the oven to 325°F (160°C).
18. Warm the cream and milk together in a small saucepan until steaming but not boiling. Remove from heat and stir in the grated Gruyère until melted and smooth.
19. In a bowl, whisk the whole egg and egg yolk together with the mustard, nutmeg and white pepper. Slowly pour the warm cheese mixture into the eggs while whisking constantly. Season with salt — be cautious, as the Gruyère adds its own saltiness.
20. Divide the sautéed mushrooms among the blind-baked tartlet shells, placing a small spoonful in each.
21. Pour or pipe the custard over the mushrooms, filling each shell to just below the rim. A small jug or squeeze bottle gives the most control for this step.
22. Bake for 12-15 minutes until the custard is just set — it should have a very slight wobble in the center when gently shaken but not be liquid. Do not overbake or the custard will lose its silky texture and become grainy.
23. Remove from the oven and let cool in the pan for 5 minutes before carefully removing the tartlets to a wire rack.

FINISH AND SERVE:
24. Pipe or spoon a small dot of carrot purée onto each warm tartlet.
25. Curl a ribbon of pickled carrot and place it on top, allowing its bright color and acidity to contrast the rich custard.
26. Finish with a micro herb or tiny thyme sprig and the lightest touch of flaky sea salt.
27. Serve warm or at room temperature. These are at their best within 30 minutes of assembly — the pastry is crispest and the custard most silky.