Spring Veggie Galette

Name: Spring Veggie Galette
Ingredients: 1 cup all-purpose flour; 0.5 cup whole wheat flour; 1.5 teaspoons white sugar; 0.5 teaspoon kosher salt; 0.75 cup chilled unsalted butter, cut into cubes; 1 egg; 1 tablespoon whole milk; 1 tablespoon olive oil; 2 shallots, thinly sliced; 2 tablespoons Dijon mustard; 0.75 cup ricotta cheese; 0.5 lemon, zested and juiced; 0.25 cup grated Parmesan cheese; salt and ground black pepper to taste; 1 pinch red pepper flakes; 8 spears asparagus, or more to taste; 0.25 cup corn; 0.25 cup peas; 1 tablespoon heavy whipping cream, or more as needed