Toss zucchini noodles with salt in a large bowl. Spread out on a layer of paper towels to absorb excess moisture.
Melt butter in a large skillet over medium heat, then stir in flour. Add minced garlic and stir until garlic is fragrant and flour has thickened, about 1 minute.
Slowly pour in cream and milk, stirring constantly, until the mixture begins to boil and thicken, 3 to 5 minutes.
Turn heat to low, stir in grated Parmesan cheese, and keep stirring until cheese is melted.
Blot zucchini noodles with more paper towels to soak up excess moisture and add zoodles to the sauce. Season with salt and pepper to taste, and warm noodles in the sauce until desired tenderness, 2 to 3 minutes.
Toss with sliced cherry tomatoes before serving and garnish with parsley.