Melt 1 tbsp butter in a large pot over medium-high heat. Cook mushrooms with a pinch of salt until golden, about 6-8 minutes, then set aside.

Reduce heat to medium, melt remaining butter, and cook onion and thyme until translucent, 5-6 minutes. Stir in garlic for 1 minute, then add flour and cook 1 minute more.

Pour in broth, add potatoes and mushrooms, and bring to a boil. Reduce to a simmer, cover partially, and cook 15-18 minutes until potatoes are fork-tender.

Remove half the soup, purée until smooth, and return to pot. Stir in milk, warm through, and season with salt and pepper.

Ladle into bowls, top with parsley and a crack of black pepper, and serve hot.