Preheat oven to 425°F.
On a large sheet pan, toss sliced mushrooms with 1.5 tbsp olive oil, salt, and pepper. Roast the mushrooms until golden brown (20 to 25 minutes, tossing halfway through).
In the meantime, bring a large pot of water to a boil. Generously salt the water, then add the pasta and give it a stir. Cook the pasta, stirring occasionally, for 1-2 minutes less than the package directions. Reserve about a cup of the pasta cooking liquid, then drain pasta. Do not rinse.
Over medium heat, add 2 tbsp olive oil to a large skillet. Once the oil heats, add 6-8 anchovies and use a wooden spoon to mash the fish into the oil. The anchovies should more or less dissolve into tiny flecks in the oil.
Once the anchovies have dissolved, add the butter and the artichoke hearts. Use a wooden spoon to break apart the artichokes as they cook. After three minutes, add the minced garlic and cook for another minute, until the garlic is fragrant.
Add the cooked pasta to the pan and stir to coat the pasta with saucy goodness. If the pasta seems too dry, add a bit of reserved pasta water to loosen it up.
Add about half of the roasted mushrooms to the pan and stir to combine.
Plate your pasta. Top with the remaining roasted mushrooms and a (heavy) sprinkle of Parmesan.