Preheat the oven to 375 degrees F (191 degrees C). Line a baking sheet with parchment paper, foil, or a silicone mat.
Remove stems from mushroom caps, and scrape out the gills if you like. Place them on the prepared baking sheet. Brush with olive oil and sprinkle with salt. Bake the mushrooms face up for 15-20 minutes, until soft.
Meanwhile, cook the sausage in a large skillet over medium-high heat for 8-10 minutes, stirring occasionally, until browned. (You can add oil to the pan if needed, but I didn't find this necessary because the sausage releases fat as it cooks.)
Reduce heat to medium. Add the minced garlic and saute for 1 minute, until fragrant. Add the marinara sauce and basil. Add salt and pepper to your taste if needed. Cook for another 2-3 minutes, until hot and not too runny.
Set the oven to the Broil setting. Drain or blot extra fluid from mushroom caps. Fill mushroom caps with sausage marinara mixture. Top with shredded cheese. Broil on the top rack for 2-3 minutes, until the cheese is melted and slightly browned.
