Heat 1 tbsp of oil in a skillet or pot over medium high. Add onion, sauté till golden at the edges, for about 5 minutes.

Add 1/2 tbsp more of oil, then add mushrooms and sauté till golden brown and any liquid is cooked off, for about 8 minutes.

Reduce heat to medium, then add remaining oil, garlic and thyme. Cook, stirring frequently, till garlic is fragrant, for about 1-2 minutes.

Stir in flour, ensuring all ingredients in the skillet or pot are evenly coated with it.

Pour in vegetable broth, salt and pepper, stirring vigorously to prevent clumps and scrape any brown bits off the skillet. Let mixture come to a boil.

Once boiling, add dried pasta. Gently stir the pasta so that they are evenly covered with liquid, and allow to cook for about 4 minutes.

Pour in milk, and allow pasta to continue to cook till al dente for about another 4 minutes, stirring occasionally. If the skillet starts to look dry, add a splash of more broth and stir gently as the pasta cooks, to avoid breaking the pasta, and also so that they do not stick to the pan.

Season with more salt and pepper if needed. Remove from heat, garnish with parmesan and parsley, then serve immediately.