Brush the pan with nonstick spray and place the mushrooms gill sides up with the stem removed. Preheat oven to 350℉.
In a small saucepan, heat olive oil over medium-low heat. Once hot, add two whole garlic cloves. Let simmer for two minutes, stirring occasionally. Don’t let the garlic cloves burn or turn too brown, it will make the oil taste bitter, rather than garlicky. Remove garlic cloves and discard.
Remove 2 tablespoons of garlic oil and set aside.
Chop the stems and add to the saucepan with the remaining garlic oil. Add shallot and 2 minced garlic cloves. Cook until soft, around 2 minutes. Stir in thyme and cook for another 30 seconds, until fragrant. Season to taste with salt and pepper. Remove from heat.
Place a spoonful of mushroom mixture into each mushroom and top with a small piece of smoked Gouda. Sprinkle a little more salt and pepper on top, if desired. Brush the outside of each mushroom with garlic oil that you set aside.
Bake for 15 minutes or until the mushrooms are soft and the cheese melts. Serve immediately.