Melt butter in a large heavy pot over medium heat. Add onion and a pinch of salt and cook, stirring occasionally with a spoon, until onion is softened and browned, about 10 minutes. Add mushrooms and carrots to pot and cook, stirring often, until mushrooms start to brown, 12–16 minutes. Add garlic, paprika, dried dill, and dried thyme and cook, stirring often, until fragrant, about 2 minutes.