Prepare the vegetables: Slice mushrooms thinly (about 0.4cm/1/6"). Cut zucchini into 0.5cm/0.2" rounds. For broccolini, cut off florets and halve them lengthwise, then slice stems diagonally into 2.5cm/1" pieces. Remove the tough string from snow peas, stack, and slice diagonally about 1cm/0.4" wide. Snap woody ends off asparagus, cut off tips, and slice stems diagonally into 2.5cm/1" pieces.

Make the creamy sauce: Melt butter in a saucepan over medium-high heat. Add heavy cream and grated Parmesan cheese. Stir until the cheese is melted and the sauce is gently simmering. Remove from heat and set aside.

Cook the pasta: Bring a large pot of generously salted water to a boil over high heat. Add linguine and cook according to package directions MINUS 1 minute (al dente is key!).

Cook the harder vegetables: While pasta cooks, add mushrooms, zucchini, broccolini stems, and asparagus stems to the boiling pasta water during the last 3 minutes of cooking time.

Cook the tender vegetables: During the LAST MINUTE of pasta cooking, add snow peas, asparagus tips, broccolini florets, green peas, and cherry tomato halves to the pot.

Combine and serve: Drain the pasta and vegetables, reserving about 1/2 cup of the starchy pasta water. Return pasta and vegetables to the pot. Pour over the reserved creamy sauce and add the minced garlic. Toss gently to combine, adding a splash of reserved pasta water if needed to reach desired consistency. Serve immediately.