Pulse mushrooms in a food processor until finely chopped. Transfer to a small bowl. Pulse cauliflower in food processor until pieces are the size of rice and transfer to a medium bowl. Pulse walnuts until finely chopped and transfer to the bowl with the cauliflower.
Add a splash of olive oil to a large heavy pot set over medium-high. Add mushrooms and cook, stirring occasionally for 4-6 minutes or until golden brown. Add garlic, oregano and another splash of olive oil. Cook, stirring occasionally, until the garlic is fragrant (about 3 minutes). Add the tomato puree, red wine and balsamic vinegar and cook for 5 minutes until reduced.
Add the cauliflower, walnuts and passata and cook, stirring occasionally, for about 30 minutes until the sauce is thickened and the cauliflower is cooked. Season with salt and black pepper then keep warm over low heat.
Cook pasta in a large pot of boiling salted water, stirring occasionally, until almost al dente, about 1 minute less than packet directions. Using a slotted spoon transfer pasta to the pot with the sauce. Add 100ml pasta water and increase heat to medium for 3 minutes or until pasta is cooked through. Remove from heat and stir in the parsley. Divide pasta among bowls and drizzle with oil.