Combine the tomatoes, onion, zucchini, garlic, vinegar, olive oil, and 1 teaspoon salt in a blender or food processor and blend or process on high until smooth or slightly chunky, depending on your preference. Season with additional salt to taste. (If desired, gazpacho can be made ahead and chilled, or all of the ingredients can be chilled before blending to reduce chilling time.)
Meanhwile, cook the tortellini according to package instructions. While the pasta is cooking, make an ice water bath: Dissolve the 1 tablespoon kosher salt in 1/2 cup warm water in a large bowl. Add 4 cups each ice and water and reserve. Drain the pasta, cool in the ice water bath for 2 minutes, then drain again.
Serve gazpacho in bowls with tortellini. Finish with a drizzle of extra virgin olive oil and shaved Parmigiano Reggiano.