Slice zucchini into thin ribbons using a vegetable peeler to create zucchini "noodles".
Heat olive oil in a skillet over medium heat; cook and stir zucchini until tender yet still with a little crunch, about 7 minutes. Season "noodles" with salt and pepper. Move "noodles" to a plate.
Melt butter in the same skillet over medium heat; add garlic and cook until fragrant, about 1 minute. Slowly add flour and whisk constantly until mixture is light brown, about 1 minute. Slowly pour in the milk while constantly whisking until a smooth sauce forms, 2 to 3 minutes.
Stir cream cheese into sauce until melted; add 1/2 cup Parmesan cheese and whisk until blended. Pour sauce of "noodles" and top with 1 tablespoon Parmesan cheese.