Make 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 in the work bowl of a food processor fitted with the plastic dough blade. Pulse to combine.
Add the yeast-water mixture to the flour and pulse to combine. Process the dough until it forms a ball and the sides of the work bowl are clean, 1 to 2 minutes.
Brush the inside of a mixing bowl with the olive oil and place the dough into the bowl. Cover the bowl 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 and set a rack in the lowest position. Lightly oil a pizza pan and set aside.
Make the pesto: Place the basil, garlic, pine nuts, salt and olive oil in the work bowl of a food processor. Pulse to combine the mixture, scrapping down the sides often.
Punch the dough down and turn it out onto a lightly floured surface. Roll the dough out to fit the pizza pan. Roll the dough to be slightly thinner in the middle and form a rim around the perimeter. If the dough is resistant to rolling, let it rest for several minutes before rolling it out again. Par-bake the crust without any toppings for 4 minutes.
Brush the top of the par-baked crust with the pesto. Top with half of the shaved Parmigiano. Bake until the cheese has melted and browned slightly, 12 to 15 minutes. Top with the remaining cheese and the sun dried tomatoes. Serve immediately.
Makes one 14-inch pizza.