Cook the spaghetti according to packet instructions. Meanwhile, melt the butter with the oil in a large, nonstick frying pan and add the bacon. Cook for 4–5 minutes, until golden.
Place the courgettes in the middle of a clean tea towel, bring up the edges and twist the tea towel over a sink to squeeze out the excess moisture. Add to the bacon with the garlic, and cook for a further 4–5 minutes, until soft and golden. Meanwhile, mix the beaten eggs in a jug with the cream, half the cheese and plenty of seasoning.
Transfer the courgette and bacon to a large mixing bowl, then toss with the drained pasta and egg mixture. Return to the frying pan and cook over a medium-low heat for 5–6 minutes. Sprinkle with the remaining cheese, then slide under a hot grill, keeping the handle away from the heat. Grill for 4–5 minutes, until golden and set. Slice into wedges and serve immediately.