Heat the broth in a pot with a lid over high heat.
Meanwhile, heat a heavy 4-quart pot over medium-high heat. Add the olive oil. When hot, add the onions and cook until softened, about 2-3 minutes. Add the garlic and cook 1 more minute. Pour in the rice and stir to coat the grains with the oil and onion mixture; cook 3-5 minute longer.
Add the wine and stir until it is almost completely absorbed by the rice. The broth should be boiling by now, so gradually add the hot broth, 1/2 cup at a time, stirring in a figure eight motion after each addition. Keep the broth pot covered, so the broth doesn't evaporate. Wait until the broth is almost completely absorbed by the rice before adding the next 1/2 cup.
After about 15 minutes, stir in the asparagus, tomatoes, and squash(or corn or carrots). Continue to add broth for about 5-10 more minutes, or until the rice is tender but firm and the vegetables are cooked.
When the rice is the desired texture, remove from heat and stir in the peas, 1/4 cup broth (if any is remaining), salt and pepper to taste, basil, and parsley. Mix in cheeses and serve immediately.