Preheat the oven to 200C/400F/Gas 6. To make the sauce, cut the tomatoes in half. Place the halved tomatoes, cut-side up, in an oiled, shallow ovenproof dish in a single layer.
Tuck the thyme and rosemary among them. Season with salt and freshly ground black pepper and sprinkle with the sugar. Drizzle over the olive and garlic infused oil.
Roast the tomatoes, uncovered, for 40-50 minutes until they're patched with brown.
Remove the thyme and rosemary sprigs, then tip the entire contents of the dish into the bowl of a food processor.
Process until fairly smooth, then pass the sauce through a sieve into a clean pan. If the sauce is a bit thick, add a little bit of water. Taste and adjust seasoning and reheat when needed.
For the omelette, remove the leaves from a few sprigs of herbs and finely chop, using a large knife. You should end up with about three tablespoons of each, chopped.
Crack the eggs into a clean bowl. Beat them energetically, adding salt, pepper, then the herbs.
Heat the lactose free butter in a wide non-stick frying pan over a medium heat until it just foams.
Add the eggs to the pan and make an omelette in the usual way, turning the pan occasionally to ensure even cooking.
As it cooks, draw the cooked eggs at the edges toward the centre of the pan, to give a plump, 'crinkled' omelette.
When it's just about cooked through, but still slightly damp and runny on top (or 'baveuse' as they say in France) dot dollops of the goats' cheese down the middle of the omelette.
Flip the sides of the omelette in toward the middle to cover. Slide the omelette out of the pan onto a warm plate. Serve the omelette with the roast tomato sauce garnished with chili and rocket if using.