Preheat oven (electric cooker: 200 °C/circulating air: 180 °C/gas: see manufacturer). Line baking tray with baking paper. Clean and hull the mushrooms and place them on the tray with the slats facing upwards. Sprinkle with oil.
Peel and chop garlic. Wash and pluck the thyme. Spread both on the mushrooms, season. Bake in a hot oven for about 10 minutes.
Beat 1 egg in each mushroom, season. Wash the tomatoes, cut them into quarters, spread around the mushrooms, season. Bake for about 10 minutes more. Wash the arugula, if necessary pluck smaller, sprinkle over it.