Bring a large pot of lightly salted water to a boil. Cook pasta at a boil, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain. Let pasta chill.
Bring a pot of lightly salted water to a boil. Add asparagus tips and cook uncovered until bright green, about 3 minutes. Drain in a colander and immediately immerse in ice water for several minutes to stop the cooking process. Drain.
Mix pasta, asparagus tips, roasted red peppers, onion, tomatoes, zucchini, yellow squash, cauliflower, fennel, and parsley in a large bowl.
Combine sun-dried tomatoes, basil leaves, Parmigiano-Reggiano cheese, mascarpone cheese, roasted garlic, salt, and pepper in a food processor. Process together and slowly add reserved sun-dried tomato oil and olive oil. Blend until dressing is smooth.
Pour dressing over pasta-vegetable mixture. Season with salt and pepper. Refrigerate for 1 hour before serving.