Heat a large skillet over medium-high heat. Add olive oil and swirl to coat bottom. Add asparagus, broccoli, mushrooms, and zucchini and saute 3-5 minutes until vegetables are tender.
Add garlic, cherry tomatoes, spinach, and peas to vegetables and cook 2-3 additional minutes until spinach is wilted. Season vegetables with salt and pepper to taste and set aside.
Cook pasta in salted boiling water until al dente. Reserve 3/4 cup pasta cooking water and drain pasta. Set aside.
Melt butter in a large skillet over medium heat. Whisk in flour and cook 1-2 minutes until golden-brown. Slowly drizzle in heavy cream and milk until smooth. Stir sauce over medium heat until bubbly and thickened. Remove sauce from heat and whisk in Parmesan, lemon zest, and basil. Season sauce with salt and pepper to taste.
Fold pasta and sautéed vegetables into sauce until evenly coated, thinning with a few splashes of pasta water as needed until sauce is loosened and clinging to pasta and vegetables. Season primavera with salt and pepper to taste and serve warm. Enjoy!