Preheat oven to 350°F. Set a cast iron pan over medium-high heat for 5 minutes.
Add 2–3 tablespoon butter to the hot pan. Once melted, add maitake mushrooms.
Season generously with kosher salt and add the smashed garlic, thyme, and rosemary. Cook for 3–5 minutes while basting until the bottom side is lightly browned.
Flip the mushrooms and continue basting for 2–3 minutes, until browned on both sides. Transfer the pan to the oven and roast for 7–10 minutes until deeply golden. Remove and set aside.
In a medium saucepan over medium heat, melt 1 tablespoon butter. Add shallots, sliced garlic, and crushed peppercorns. Cook 4–5 minutes, stirring often, until softened but not browned.
Optional: Carefully add cognac and flambé (or simmer until reduced by half), scraping up any bits from the bottom.
For a smoother sauce, blend the mixture then return to pan.
Add heavy cream and bring to a gentle simmer. Cook until the sauce coats the back of a spoon, about 1–2 minutes.
Season with kosher salt to taste.
Plate the roasted maitake and spoon sauce generously over the top. Finish with flaky salt and serve hot.