Use a pastry brush, or damp paper towels, to remove surface dirt from your mushrooms. Remove the stems from the shiitakes. Thinly slice your shallots and mushrooms.
Add olive oil to a cast iron pan or large skillet set over medium-high heat. Once the oil is shimmering, add the butter. When the butter melts and begins to foam add your sliced mushrooms and shallots.
After about 2 to 3 minutes, the mushrooms will begin to release liquid. When this has almost completely evaporated, add in your whole stems of rosemary and thyme.