Preheat oven to 450 degrees F. Boil noodles according to package directions and drain while reserving 1/2 cup of the cooking water.
Chop cauliflower into 1 - 2 inch florets (discarding large stems). Toss on a baking sheet with garlic, olive oil, thyme, pepper, and lemon juice. Bake until the cauliflower just begins to turn brown and is easily pierced with a fork, about 20 - 22 minutes, stirring once or twice.
To toast the walnuts, add them to the baking sheet with the cauliflower and put it all back in the oven for 2 - 3 minutes while keeping a close eye on it because they can go from brown to burnt very quickly!
Meanwhile, toss the noodles with the reserved cooking water, Parmesan cheese, heavy cream, and salt. Stir in the cauliflower mixture and heat on medium-low until the sauce thickens. Divide among pasta bowls, garnish with parsley if desired, and serve warm.