Mix all-purpose flour, whole wheat flour, sugar, and 1/2 teaspoon kosher salt together in a food processor. Add cubed butter; pulse until mixture is the size of peas.
Whisk 1 egg and milk together in a small bowl. Add to the food processor; pulse until dough clumps together.
Turn dough out onto a sheet of plastic wrap. Bring together into a ball; flatten into a disk and chill until firm, at least 1 1/2 hour and up to overnight.
Remove dough from the refrigerator. Let come to room temperature, about 1 hour.
Preheat oven to 425 degrees F (220 degrees C).
Heat oil in a large skillet over medium heat. Add shallots; cook and stir until translucent and edges are browned, about 3 minutes. Remove from heat; let cool.
Unwrap dough and place on a work surface lined with parchment paper. Roll out into an 11-inch circle. Slide dough and parchment paper onto a baking sheet. Spread mustard over dough, leaving a 1-inch border.
Mix ricotta cheese, 1 egg, lemon zest, lemon juice, Parmesan cheese, salt, pepper, and red pepper flakes together in a bowl. Spread over mustard. Scatter shallots, asparagus, corn, and peas on top.
Lift corners of the parchment paper up to help fold the edges of the dough around the filling; gently pleat to seal. Brush heavy cream over edges of the dough.
Bake in the preheated oven until golden, about 35 minutes.
