Heat oven to 375° with rack in middle.

Make the dough: In a large bowl, combine all-purpose flour, whole-wheat flour and salt. Add butter; rub in with fingertips until mixture resembles coarse meal. Mix in egg yolks, then add 2 tablespoons ice water; mix dough together with hands (do not overwork). Divide dough into 4 equal pieces; form each piece into a ball and press each into a 4-inch disc. Individually wrap discs tightly in plastic wrap and refrigerate until firm, about 30 minutes. 

Shape and bake the crust: On a well-floured work surface, roll out 1 disc of dough to a 7-inch round. Fit dough into a tart pan, letting excess hang over edge. Fold overhang inward and press against side of pan to reinforce edge. Repeat with remaining dough and pans. Lightly prick the bottom of shells all over with a fork and chill for 10 minutes in the freezer.

Line chilled shells with pieces of parchment paper or aluminum foil, leaving a 1-inch overhang. Fill with pie weights or dried beans. Bake until edges of crusts are just beginning to turn golden brown, 10 to 15 minutes. Remove parchment and pie weights. Rotate crusts, return them to the oven and continue baking until bottoms are dry and edges lightly golden, 12 to 15 minutes more. Transfer tart shells to a wire rack to cool completely. Increase oven temperature to 400°. 

Make the filling: While the tart shells are cooling, bring a large pot of salted water to a boil. Add asparagus and cook until tender, about 5 minutes; drain and pat dry. Cut into 1 1/2-inch lengths. In a bowl, whisk together eggs, egg yolks and milk.

Assemble and bake the quiches: Put cooled tart shells on a baking sheet; fill with spinach and asparagus, then ladle egg mixture over the top. Sprinkle with generous pinch salt and cheese. Bake until filling is puffed and lightly golden, about 25 minutes. Cool tarts on a wire rack 15 minutes, then remove from pans. Serve warm or at room temperature.