Make the brioche dough: Combine flours, milk powder, sugar, yeast, eggs, and ⅓ c. plus 1 Tbsp. water in a stand mixer fitted with a hook attachment. Add salt, then mix on medium speed until full gluten development, 18–20  minutes. (To check this, take a piece of dough, toss it in flour, then take your fingers and slowly stretch dough out. You want to be able to almost see through dough without it tearing.)

On low speed, begin adding butter to dough, piece by piece.

Once butter has almost fully incorporated, increase speed back to medium-high, and mix for another 8–10 minutes. You want dough to clear bowl and make a slapping noise.

Transfer to a greased bowl, cover, and let sit at room temperature for 1 hour.

Degas dough by punching down and folding in half once.

Chill, covered, in fridge at least 8 hours, but overnight is best.

Make the mushroom cream: Warm oil and butter in a Dutch Oven or Saute Pan over medium-low heat  until melted.

Add onion and garlic, season with salt and pepper, and cook until translucent, 5–7 minutes.

Add mushrooms and increase heat to medium. Season with salt and pepper. Once mushrooms have released water, increase heat to medium-high. Keep cooking until all ingredients have started to take on color, 5–7  minutes total.

Add cream and milk. Using cooking twine to tie bay leaf and thyme in a bundle and add to Dutch Oven. Bring to a simmer and cook for 15 minutes. Allow to cool slightly. Discard bay leaf and thyme bundle and stir in chèvre.

Transfer to a blender and purée until smooth.

Season with salt and pepper and chill until needed.

Prep the toppings: Preheat oven to 375F. Quarter potatoes and slice mushrooms. Toss with oil, salt, and pepper and roast on Baking Slabs or Sheet Pans until tender and cooked through, 15-20 minutes. (They will cook more once on the tart.)

Make the egg wash: Combine egg, egg yolk, milk, and salt in a medium bowl. Beat with a fork to combine.

To assemble and bake: On a lightly floured surface, roll out brioche to roughly size of Baking Slab with 1 ½–2” excess dough hanging off sides. Transfer to Baking Slab and fold excess dough underneath itself to create a clean edge.

Cover with plastic wrap and let proof at room temperature until doubled in size, about 1 hour (can take longer depending on ambient temperature).

Once dough has proofed for about 40 minutes, preheat oven to 350F.

Spread ½ cup mushroom cream over dough using a small offset spatula, leaving about a ½” border of dough.

Evenly layer chorizo and roasted potatoes and mushrooms over top of cream.

Scatter quesillo over top (be mindful that cheese will help adhere any toppings that might not be in contact with the mushroom cream).

Brush edges with egg wash and sprinkle with pepper around border.

Bake until cheese is melted and dough is deep golden brown, 20–25 minutes.

Brush edges with melted butter immediately out of oven. Top with thyme, parsley, and/or chives, and serve with lemon wedges.