To make the pesto: Clean out the food processor and then combine the basil, arugula, garlic and pine nuts in the bowl. Pulse until the ingredients are coarsely chopped. With the food processor running, slowly pour the olive oil into the bowl through the feed tube, and process until the pesto is thoroughly pureed. Season with salt and pepper and pulse a few more times. Add the Pecorino cheese and puree until the cheese is thoroughly combined. Transfer the pesto to a jar with a lid or covered bowl until ready to use. The pesto can be made several days ahead and kept refrigerated.

To assemble the galette: Preheat the oven to 375 F and line a baking sheet with parchment paper or a Silpat. Remove the disk of pie dough from the refrigerator and place it on a lightly floured work surface. Dust some flour on the rolling pin, and roll out the dough to a large circle, about 12 inches in diameter. (If your dough was refrigerated for more than a half an hour, wait about 20 minutes before rolling.)

Using your rolling pin and starting on one end of the dough, loosely roll up your pie crust around the rolling pin. Transfer it to the prepared baking sheet and roll the dough back out flat.

Spread about 1/3 cup of pesto in the center of the dough, leaving about a 1 1/2- to 2-inch border all around the edge. Lightly drizzle on just a touch of extra-virgin olive oil over the pesto. Arrange your sliced summer squash, zucchini and tomatoes in a single layer over the top, arranging them however you want.

Gently fold the pastry border over the vegetables, overlapping the edges as much as possible and creating pleats all around the edges. Brush the folded edges of the crust with the egg wash.

Bake for 35 to 40 minutes, or until the crust is golden brown. Let the galette cool for at least 5 to 10 minutes before serving, and garnish with freshly grated pecorino cheese. Serve the galette with the leftover pesto if desired.

Recipe Notes

Make Ahead: You can easily make the pesto and the all-butter dough the day or two before and refrigerate both. For the pesto, make sure you cover your pesto with a thin layer of extra virgin olive oil and cover with plastic wrap or store in a jar with a tight lid. When ready to use the both the dough and the pesto, take out of the fridge and leave on the counter for about 20 minutes.

For the crust: I recommend using a food processor, which saves time, but if you don't have one, simply use a pastry blender to break up and combine the cold butter with the flour. This method will take longer.

For the pesto: if you don't like arugula, you can simply use all basil leaves or try basil plus baby spinach. Pesto is so versatile, experiment and see what you like.

I used my mandolin slicer to quickly slice the yellow summer squash and zucchini; this also ensures that the vegetables are the same thickness.

(Alice Choi is a writer for TheKitchn.com, a nationally known blog for people who love food and home cooking. Submit any comments or questions to kitchn@apartmenttherapy.com.)