Melt butter with olive oil in a large frying pan.
Add courgettes and cook, stirring frequently over medium-high heat, until just golden, 10 minutes.
Reduce heat to medium-low.
Add garlic and cook, stirring occasionally, until courgettes are soft, 5-10 minutes.
Add cream and simmer gently until just thickened, 2 minutes.
Add basil with salt and pepper to taste.
Meanwhile, cook pasta in a large pot of boiling, salted water, until firm to the bite.
Add pasta with parmesan to the hot sauce.
Toss well to coat.
Serve immediately with additional parmesan.