In a large pot over medium heat, melt the butter. Add chopped onions and minced garlic; cook until translucent and fragrant, about 3–4 minutes.

Add sliced mushrooms and fresh thyme; cook over medium-high heat until mushrooms are golden brown and liquid has evaporated, about 8–10 minutes.

Sprinkle flour over the mushrooms and stir well to coat. Cook for 1–2 minutes until the flour is golden.

Gradually pour in the chicken or vegetable broth, stirring constantly. Bring the mixture to a gentle simmer, then reduce heat and cook for about 10 minutes.

Remove the pot from heat and carefully blend until smooth, leaving a few mushroom pieces for texture.

Return to low heat and stir in heavy cream, simmering for 2–3 minutes. Adjust seasoning with salt and pepper to taste.