Pulse the all-purpose flour, whole-wheat flour, and cold butter cubes in a food processor until the mixture resembles coarse breadcrumbs with pea-sized pieces of butter throughout—this creates the flaky texture we want. Add the ice water a tablespoon at a time, pulsing gently until the dough just begins to hold together when squeezed; be careful not to overwork it or the crust will be tough. Form the dough into a disk, wrap it in plastic, and refrigerate for at least 1 hour. I always make my pastry dough ahead of time because it gives the gluten a chance to relax, which makes rolling much easier.

While the dough chills, slice the leeks into 1/4-inch rounds, then wash them thoroughly to remove any trapped soil between the layers. Trim the tough, woody ends from the asparagus and cut the spears into 2-inch pieces. Heat 2 tablespoons of butter with 1/2 teaspoon of salt in a large skillet over medium heat and cook the leeks for about 10 minutes, stirring occasionally, until they're completely tender and lightly golden. This slow cooking sweetens the leeks and drives off excess moisture, which is essential for keeping the galette crust crisp. Set the cooked leeks aside to cool slightly.

In a bowl, combine the drained ricotta, 1/2 cup grated parmesan, and a pinch of nutmeg, stirring gently until just combined. The nutmeg adds warmth and sophistication to the filling without being obvious—it's a technique I borrowed from Italian pastry chefs. Set aside until ready to assemble.

Preheat your oven to 400°F. Remove the dough from the refrigerator and let it sit at room temperature for about 20 minutes to make it more pliable for rolling. Place the dough between two sheets of parchment paper and roll it out into a 14-inch circle, rotating the parchment as you go to ensure even thickness. Transfer the dough on its parchment to a baking sheet. Brush the entire surface of the dough lightly with 2 tablespoons of olive oil, leaving a 1.5-inch border uncovered—this helps the crust brown evenly and stay crispy.

Spread the ricotta mixture from Step 3 evenly over the oiled dough, stopping 1.5 inches from the edge. Layer the cooked leeks from Step 2 over the ricotta, then arrange the raw asparagus pieces on top in a slightly overlapping pattern—the asparagus will cook gently in the oven while the crust bakes. Fold the dough border up and over the filling, creating loose, rustic pleats as you go around; it should partially cover the filling with a rough, imperfect appearance. In a small bowl, whisk together 1 egg and 1 tablespoon of cream, then brush this egg wash over the exposed dough border to give it a golden, glossy finish when baked.

Place the galette in the preheated 400°F oven and bake for 40 minutes, or until the crust is deep golden brown and the asparagus is tender when pierced with a fork. The pastry should smell nutty and delicious as it bakes. Remove from the oven and let cool for 5 minutes.

While the galette is still warm, scatter the torn burrata cheese over the top, allowing it to soften slightly from the residual heat. Drizzle generously with balsamic glaze in a crosshatch pattern, then finish with a sprinkle of flaky salt and freshly ground black pepper. Slice into wedges and serve warm or at room temperature—this galette is wonderful either way.