Adjust oven rack to lower-middle position and preheat to 400°F. Spread asparagus-leek mixture on prepared dough round, leaving about a 2-inch border of dough all around. With a sharp knife, cut a series of slits in the border of dough, each running from filling to edge of dough, spacing them about 5 inches apart. Fold each segment of dough over filling, tugging gently so the edge of each segment tightly overlaps the one that came before. Chill galette for 10 minutes in the refrigerator.
In a small bowl, drizzle reserved asparagus tips with olive oil, season with salt, and toss to coat lightly and evenly. Arrange asparagus tips on top of exposed filling in center of the galette.
Brush egg over chilled dough in a thin, even layer (including under each flap). This will give the crust a glossy, golden sheen and help bind the pieces together.
Bake until galette is golden brown around the edges and bubbling in the center, about 45 minutes longer. Let cool 5 minutes, then slice into wedges and serve warm.
Special equipment
Large sauté pan, large saucepan or saucier
Make-Ahead and Storage
The galette can be held at room temperature (and served warm or at room temperature) for a few hours after making. Leftovers can be wrapped in plastic and refrigerated, then reheated in a warm oven.
