Cook the pasta in plenty of boiling salted water for 10-12 minutes until al dente. Clean and wash broccoli and cut into florets. Cook for about 5 minutes. Drain both.
Wash the thyme and pluck the leaves off. Whisk eggs, cream and milk together. Season with salt and pepper and thyme.
Peel and chop the garlic. Finely dice the bacon and fry in a large pan without fat until crispy. Sauté the garlic. Add the pasta and broccoli and toss briefly.
Put everything in a greased baking dish. Pour egg cream over it. Grate the cheese, sprinkle over it. Spread 1 tablespoon of butter in flakes over the top. Bake in a preheated oven (electric stove: 200 ° C / convection: 175 ° C / gas: level 3) for 30-35 minutes. Possibly cover up towards the end.