Preheat the oven to 200°C.
Arrange halved tomatoes cut-side up in an oiled ovenproof dish.
Add garlic, thyme, and rosemary then season with salt, pepper, and sugar.
Drizzle with olive oil and roast for 40 to 50 minutes until browned.
Discard herb sprigs and blend the remaining dish contents in a food processor.
Pass the sauce through a sieve into a pan and adjust consistency with water if needed.
Finely chop the fresh herbs and beat them into the eggs with salt and pepper.
Heat butter in a frying pan and cook the egg mixture while drawing edges to the center.
Add goat cheese to the center when the eggs are still slightly runny.
Fold the omelette over the cheese and serve immediately with the tomato sauce.