Heat oil in a large saucepan over medium-high heat. Once shimmering, add onion, garlic and mushrooms. Season with salt and pepper and cook stirring occasionally until onions are just starting to brown.
Add tomatoes, thyme, anchovy paste, and 1/2 cup of water and bring to a boil. Reduce heat to a low simmer and cook until slightly thickened, about 30 minutes.
While sauce is simmering, bring a large pot of heavily salted water to a boil. Once boiling, add pasta and cook according to package instructions. Remove pasta from cooking water into sauce and toss to combine, if sauce seems too thick add a ladle or two of pasta water. Taste and add more salt if necessary. Serve with grated parmesan cheese over the top.