Toss the sliced beets with 2 tablespoons olive oil and a pinch of salt. Place in a single layer on a prepared baking sheet and bake in the oven until fork tender, 10-12 minutes. Remove from oven and set aside.
While the beets cook, prepare the pesto. Place the beet greens, garlic, walnuts, salt, and pepper in the bowl of a food processor. Pulse until finely chopped. With the motor running slowly, drizzle in the olive oil. Continue to process until smooth, adding more oil if necessary to achieve a saucy consistency. Taste and add additional salt and pepper if desired.
Roll out your dough to a 12-14-inch circle on a floured surface. Evenly spread the pesto on the crust, followed by the beets and goat cheese. Place the pizza in the oven and bake until the crust is just beginning to turn golden, 8-10 minutes. Remove the pizza from the oven and sprinkle with the walnuts. Continue cooking until the crust is golden brown, the cheese is melted, and the walnuts are golden and crisp, about 2 more minutes.
Serve the pizza with mixed spring greens and a drizzle of extra virgin olive oil.