Place the flours and the salt in the bowl of a food processor fitted with the blade attachment and pulse to combine.

Add the butter and pulse until the largest pieces are the size of small peas.

Sprinkle four tablespoons of the ice water onto the dough. Pulse until the dough begins to hold together. Add the additional tablespoon of water and continue to pulse if the dough is otherwise too dry to hold together.

Turn the dough out onto a piece of waxed paper and shape into a disc by pressing quickly and firmly with your hands, repairing any cracks as you go. Wrap the dough in the waxed paper and refrigerate for 30 minutes.

Preheat the oven to 375°F with a rack in the center.

On a lightly floured surface, roll out the dough into a 12-inch-diameter circle about ¼-inch thick.

Press into the bottom and sides of a fluted 10-inch tart pan with a removable bottom. Roll your rolling pin over the top of the pan to remove any excess dough.

Prick the bottom of the dough all over with a fork, then line the dough with parchment paper and fill with dried beans.

Place the tart pan on a baking sheet. Bake for 10 minutes, then remove the parchment and beans and bake for 7 minutes more.

While the dough bakes, make the filling. Beat the eggs in a medium mixing bowl. Add the ricotta, lemon thyme, salt, and pepper and beat until well combined. Stir in the sliced scapes.

Pour the filling into the partially baked tart shell and return the whole thing to the oven for about 25 minutes, until the filling is set.

Cool to warm or room temperature before slicing and serving.