Heat the oil in a frying pan. Sauté the garlic for 1 minute over low heat while stirring.
Add the mushrooms and stir to coat well with fat.
Mix the wine and tomato paste in a bowl and pour it over the previous preparation. Add half of the thyme. Add salt and pepper. Cook over low heat, stirring occasionally, for 15 to 20 minutes: almost all the liquid should have evaporated and the mushrooms should be juicy and glossy.
Transfer to a serving dish. Serve hot, warm or at room temperature, sprinkled with the remaining thyme.