Pasta with Mushroom Ragu

Serves 3

6 Tbsp. extra-virgin olive oil 

1 medium onion, finely chopped 

Kosher salt 

12 garlic cloves, thinly sliced 

1/2 cup double-concentrated tomato paste 

24 oz. mixed mushrooms (such as crimini, shiitake, oyster, and/or maitake), tough stems trimmed, coarsely chopped 

1/2 cup heavy cream 

Freshly ground black pepper 

24 oz. rigatoni or other short pasta 

3 Tbsp. unsalted butter 

2 oz. Parmesan, finely grated (about 1 cup), plus more for serving