Pasta With Lentils and Mushrooms

Name: Pasta With Lentils and Mushrooms
Ingredients: ¼ cup olive oil; 1 medium onion, finely chopped; 8 oz. crimini mushrooms, stems trimmed, chopped into ¼ pieces; 1 tsp. kosher salt, plus more; 2 garlic cloves, coarsely chopped; 1 cup brown lentils, rinsed; ¼ cup double-concentrated tomato paste; ½ tsp. crushed red pepper flakes; 10 oz. orecchiette or conchiglie; 1½ oz. Parmesan, finely grated (about ½ cup), plus more for serving; 3 Tbsp. unsalted butter, cut into pieces; ½ cup coarsely chopped parsley, plus more for serving