Make the Rhubarb-Strawberry Compote (Day Before or First):
Combine rhubarb, strawberries, sugar, lemon juice, and water in a medium saucepan.

Cook over medium heat, stirring occasionally, until fruit breaks down completely and mixture is thick and jammy, 15-20 minutes. It should coat a spoon thickly.

Remove from heat and cool completely. Divide into portions: 3 tablespoons for dough, 3-4 tablespoons for icing (strain these through a fine-mesh sieve), remainder for optional filling or serving.

Make the Brioche Dough:
In the bowl of a stand mixer fitted with the dough hook, combine flour, sugar, yeast, and salt. Whisk briefly to distribute.

Add eggs and lukewarm milk. Mix on low speed until a shaggy dough forms, about 2 minutes.

Increase speed to medium and knead for 8-10 minutes until dough is smooth, elastic, and pulls away from the sides of the bowl. It will be quite sticky—this is normal for enriched dough.

With mixer running on medium-low, add softened butter one or two cubes at a time, allowing each addition to incorporate before adding more. This takes 8-10 minutes total. The dough will look broken and messy initially, then come back together into a smooth, glossy, elastic dough.

Add 3 tablespoons rhubarb-strawberry compote and a small amount of pink gel coloring if desired. Mix until color is evenly distributed.

Transfer dough to a lightly oiled bowl, cover tightly with plastic wrap, and refrigerate overnight (or at least 4 hours). Cold fermentation develops flavor and makes the enriched dough easier to handle while ensuring proper gluten development.

Shape the Buns:
Line two baking sheets with parchment paper.

Turn cold dough onto a lightly floured surface. Divide into 12 equal pieces (about 85g each). Working with one piece at a time, shape into smooth ovals approximately 5 inches long—traditional finger bun shape.

Place shaped buns on prepared sheets, spacing 2 inches apart. Cover loosely with oiled plastic wrap.

Let buns rise in a warm place (75-80°F) until doubled in size and dough springs back slowly when gently poked, 1½-2 hours. Do not rush this. Aaron identified underproving as his likely issue; properly proved buns will be pillowy-soft. If the indent springs back immediately, they need more time.

Bake the Buns:
Preheat oven to 350°F (175°C) during the final 30 minutes of proving.

Bake 14-16 minutes until buns are pale golden on top and sound hollow when tapped on the bottom. Do not overbake—enriched doughs dry out quickly. The internal temperature should reach 190°F (88°C).

Cool on baking sheets 5 minutes, then transfer to wire racks to cool completely.

Make the Vanilla Crème Pâtissière:
Heat milk with vanilla bean (seeds and pod) in a medium saucepan until steaming and just beginning to bubble at edges. Remove from heat, cover, and steep 15 minutes.

In a medium bowl, whisk egg yolks and sugar until pale and slightly thickened, about 2 minutes. Whisk in cornstarch and salt until smooth.

Remove vanilla pod from milk. Slowly pour about half the hot milk into the yolk mixture, whisking constantly to temper.

Return everything to the saucepan. Cook over medium heat, whisking constantly, until mixture thickens and comes to a boil. Continue whisking for 1 full minute after it boils to cook out the starchy taste.

Remove from heat. Whisk in cold butter until smooth and glossy.

Transfer to a shallow dish, press plastic wrap directly onto surface, and refrigerate until cold and set, at least 2 hours.

Before using, whisk crème pat until smooth and pipeable. Transfer to a piping bag fitted with a long filling tip.

Fill the Buns:
Using a sharp knife, cut a slit along the top of each bun, going about two-thirds of the way down but not cutting through the bottom.

Pipe or spoon crème pâtissière generously into each bun. Optionally, add a small spoonful of rhubarb-strawberry compote alongside the cream.

Make the Icing:
Whisk sifted powdered sugar with strained rhubarb-strawberry compote until smooth and thick but pourable—it should ribbon off the whisk and hold briefly before sinking back. Add milk one teaspoon at a time if too thick, or more powdered sugar if too thin.

Add pink gel coloring if a more vibrant hue is desired.

Ice the Buns:
Dip the top of each filled bun into the icing, or spoon icing over the top, allowing it to drip slightly down the sides.

While icing is still wet, garnish with freeze-dried strawberry pieces and edible flower petals if using.

Let icing set at room temperature, about 20 minutes.