Cook pasta according to package directions, adding broccoli and asparagus or green beans for the last 3 minutes of cooking. Drain.
Meanwhile, place a fine strainer over a large bowl. Cut tomatoes in half; squeeze seeds and juice into strainer. With the back of a spoon, press seeds against strainer to extract juice; discard seeds. Chop tomatoes. Add ricotta cheese, basil, snipped thyme, balsamic vinegar, oil, garlic, salt, and pepper to tomato juice; mix well. Stir tomatoes into ricotta mixture.
Add hot pasta-vegetable mixture to ricotta mixture. Toss to coat all ingredients. Divide mixture among 4 dinner plates; sprinkle with Parmesan or Romano cheese. If desired, garnish with basil sprigs.