6 Large, stemmed and wiped with a damp paper towel (6 Large Ones)
Extra virgin olive oil
1. Combine butter, cheese, thyme, and 1/8 teaspoon of the pepper in a small bowl, mashing with a fork to blend completely. Roll into a 3-inch log; wrap in plastic and refrigerate.
2. Prepare a high-heat grill.
3. Brush mushrooms on both sides with oil; season with salt and remaining 1/8 teaspoon pepper. Grill mushrooms, gill-side up, for 6 minutes. Flip and cook until firm to the touch with a bit of give, about 6 minutes longer. (If you cut into one to check for doneness, the inside should look moist.)
4. Cut butter into 6 slices. Serve mushrooms gill-side down, topped with seasoned butter.