Add the olive oil to a skillet on medium heat and once hot add the mushrooms.
Cook the mushrooms and garlic for about 5 minutes, stirring occasionally, until browned.
Move the mushrooms aside and add the butter and flour and stir on the side until melted and mixed.
Add the cooking wine and simmer until most boiled off, about 7 minutes.
Add the vegetable broth, half-half, thyme, salt and pepper and bring to a boil.
Once boiling, turn the heat to low and simmer and stir until thick.