Make pesto. Place garlic in food processor or blender and process for 30 seconds. Add basil leaves and process for 1 minute, until leaves are chopped. Add Parmesan cheese, pine nuts, ¾ teaspoon salt, and ¼ teaspoon pepper and process for 30 seconds. While processor is running, slowly drizzle in ⅓ cup olive oil and process until smooth. Set aside.
Bring large pot of salted water to a boil. Trim off one end of each zucchini. Use a spiralizer to cut zucchini into noodles. Heat 1 tablespoon olive oil in large skillet over medium heat. Add red pepper flakes and sauté for 1 minute, careful not to burn. Add zucchini noodles to skillet and sauté for 3 to 4 minutes, being careful not to overcook, as they will get watery. Season with salt and pepper to taste and remove from heat.
Add spaghetti to pot of boiling water and cook uncovered until pasta is al dente. Drain pasta and add to zucchini mixture in skillet. Add pesto to pasta-zucchini mixture and stir to combine. To serve, divide onto four plates. Top each portion with 2 tablespoons ricotta, then drizzle ½ tablespoon olive oil over each.