For the dough:
In a small bowl, dissolve the yeast in the warm water, whisk in the honey and let sit until the mixture is foamy, about 10 minutes. Whisk in the olive oil. Place the flour and salt into the work bowl of a food processor fitted with the plastic dough blade. Pulse to combine.
Pour in the yeast mixture and pulse to combine. Process the dough until it forms a ball and the sides of the work bowl are clean, about 1 to 2 minutes.
Brush the inside of a mixing bowl with olive oil and place the dough in the bowl. Cover with plastic wrap and let the dough rise in a warm, draft-free place until doubled in size, 60 to 90 minutes.
Preheat an oven to 500 F with the rack positioned in the lowest position. Lightly oil a pizza pan and set aside.
When the dough has risen, punch it down and turn it onto a lightly floured work surface. Divide the dough into 4 equal pieces. Set 2 pieces of dough aside and cover loosely with plastic wrap. Roll or stretch the remaining pieces of dough into a slightly oval shape (about half the size of the pizza pan). Place the stretched dough onto the prepared pizza pan.
For the topping:
Sprinkle 1/4 of the cheese, 1/4 of the sliced beets and 1/4 of the chopped walnuts over the dough. Lightly drizzle with olive oil and season to taste with salt and pepper. Bake until the cheese has melted and the walnuts have toasted, 10 to 12 minutes. Repeat with the remaining pieces of dough.
Toss the mixed greens with 1 tablespoon olive oil and salt and pepper to taste. Place a portion of the greens on top of each piadini. Serve immediately.
Makes 4 piadinis