Make the gravy. Melt 2 tablespoons of butter in a large nonstick skillet over medium flame. Add diced mushrooms and toss to coat with butter. Add fennel seeds, thyme and red pepper flakes. Season with salt and black pepper, being generous with the pepper. Toss to combine and cook mushrooms, stirring frequently, until browned, tender and slightly cooked down in volume, about 5 minutes. Add coffee and cook until almost evaporated, stirring frequently, 1 to 2 minutes.
Transfer mushroom mixture to bowl and set aside. Do NOT wipe skillet. Melt remaining 1-1/2 tablespoons of butter in skillet and sprinkle in flour. Cook, whisking continuously, until flour and butter combine and flour browns slightly, 2 to 3 minutes.
Stir in milk and bring to a boil. Return mushrooms to the skillet. Reduce heat to low and cook until gravy thickens, stirring occasionally, 5 to 10 minutes. A skin will occasionally form on the top of the gravy as it thickens; just stir it back into the gravy. Taste and adjust seasonings. You want the gravy on the salty side and with plenty of pepper, so don't skimp here. When biscuits are ready, split one (or more) open on each plate and spoon gravy over.
Make the biscuits. Preheat oven to 475ºF. Line a baking sheet with parchment paper (or else lightly grease a baking sheet). Melt butter in a small saucepan, then transfer to a small bowl to cool slightly. Mix dry ingredients in a large mixing bowl.
Pour chilled buttermilk into a 2-cup measuring cup. Add melted butter and stir until clumps form. Stir buttermilk mixture into flour mixture with a rubber spatula just until the ingredients are incorporated. At first, it may seem as if you need more liquid. You don't. Just keep scraping the bottom of the bowl until you’ve worked all the flour into the dough.
Using a greased 1/3-cup measure, scoop mounds of dough and drop them onto baking sheet, spacing about 1-1/2 inches apart. Press on them with your fingers to slightly flatten and form into a biscuit shape. Bake biscuits until the tops are golden brown, 10 to 14 minutes. Remove from oven and let rest on the baking sheet for a few minutes.