Day One: Make the Détrempe (Base Dough)
Combine dry ingredients: In the bowl of a stand mixer, whisk together flour, sugar, salt, and instant yeast.

Add wet ingredients: Add cold milk, cold water, egg, and softened butter. Using the dough hook, mix on low speed until a shaggy dough forms, about 2 minutes. Increase to medium speed and knead for 5-6 minutes until smooth and slightly tacky but not sticky.

Shape and chill: Turn dough onto a lightly floured surface and shape into a rough rectangle. Wrap tightly in plastic wrap and refrigerate overnight (or at least 4 hours). This rest allows gluten to relax and dough to chill thoroughly—essential for successful lamination.

Day One: Prepare the Butter Block
Create the butter block: Place cold laminating butter between two sheets of parchment paper. Using a rolling pin, pound and roll butter into a 6×8-inch rectangle of even thickness. Keep cold but pliable—it should bend without cracking or becoming soft and greasy. Refrigerate until needed.

Day Two: Laminate the Dough
Roll out the détrempe: Remove dough from refrigerator. On a lightly floured surface, roll into a 12×8-inch rectangle, with a short side facing you.

Enclose the butter: Place butter block on bottom two-thirds of dough rectangle, leaving ½-inch border on three sides. Fold top third (without butter) down over middle third, then fold bottom third up and over, like a business letter. Press edges to seal. You've completed your first turn.

First rest: Wrap dough in plastic and refrigerate 30 minutes.

Second turn: With seam side facing right (like a book), roll dough into a 12×8-inch rectangle again. Fold in thirds as before. This is your second turn. Mark dough with two finger indentations to remember how many turns completed.

Second rest: Wrap and refrigerate 30 minutes.

Third and fourth turns: Repeat rolling and folding process two more times, resting 30 minutes between each turn. After fourth turn, refrigerate dough for at least 1 hour (or overnight).

Day Two: Make the Za'atar Filling
Prepare the za'atar paste: In a small bowl, combine za'atar spice blend with olive oil. Stir to form a loose paste. Set aside.

Make the cheese filling: In a medium bowl, combine grated Gruyère, softened cream cheese, egg yolk, minced garlic, and black pepper. Mix until well combined. Taste and add salt only if needed—Gruyère is naturally salty.

Day Two: Shape the Swirls
Roll the dough: On a lightly floured surface, roll chilled laminated dough into a rectangle approximately 16×12 inches and about ¼-inch thick. Keep edges as straight and even as possible.

Apply the fillings: Spread za'atar-oil paste evenly over entire surface of dough, leaving ½-inch border along one long edge. Crumble or dollop cheese mixture evenly over za'atar layer.

Roll into a log: Starting from long edge opposite the border, roll dough tightly into a spiral log. When you reach the border, brush it lightly with water and press to seal.

Cut the swirls: Using a sharp knife or bench scraper, trim uneven ends (baker's treat). Cut log into 12 equal pieces, approximately 1¼ inches each.

Arrange for proofing: Place swirls cut-side up on parchment-lined baking sheets, spacing 2 inches apart. Cover loosely with plastic wrap.

Proof and Bake
Proof the swirls: Let rise in a warm spot (about 75°F/24°C) until noticeably puffed and layers look distinct, about 1½-2 hours. Don't rush—underproofed Danish will be dense and lamination won't show.

Preheat and prepare: Preheat oven to 400°F (200°C). Make egg wash by beating together egg and milk.

Apply egg wash and toppings: Gently brush tops of swirls with egg wash, being careful not to deflate them. Sprinkle with sesame seeds and light touch of flaky sea salt. For extra za'atar presence, add a tiny pinch of additional za'atar on top.

Bake: Bake 18-22 minutes, rotating pans halfway through, until swirls are deep golden brown and cheese is bubbling and beginning to caramelize at edges. Laminated layers should be visibly puffed and distinct.

Cool briefly: Transfer to wire rack and let cool 5-10 minutes. Serve warm for best experience.