Bring a large saucepan of water to a boil. Cook 8 ounces rotini according to package directions for al dente. Reserve ½ cup cooking water; drain the pasta.
Meanwhile, melt 2 tablespoons butter in a large nonstick skillet over medium heat. Add cauliflower florets and ¾ teaspoon salt in an even layer. Cook, undisturbed, until browned on the bottom, 5 to 7 minutes. Stir; cook, stirring occasionally, until golden brown all over, 5 to 8 minutes.
Add ¼ cup garlic; cook, stirring occasionally, until fragrant, about 1 minute. Add 2 tablespoons water, 2 teaspoons thyme, ¾ teaspoon pepper and the remaining 1 tablespoon butter; cook, stirring occasionally, until the cauliflower is well coated, about 2 minutes.
Stir in 2 tablespoons vinegar; cook, stirring often, until the liquid has mostly evaporated, about 30 seconds. Remove from heat.
When the pasta is done, return the cauliflower mixture to medium heat; stir in the cooked pasta, the reserved ½ cup cooking water, ½ cup sour cream, ¼ cup heavy cream and ¼ cup Parmesan. Cook, stirring constantly, until the sauce becomes creamy and coats the pasta, 1 to 2 minutes.
Divide among 4 bowls. Top with the remaining ¼ cup Parmesan. Garnish with additional thyme leaves and pepper, if desired.
