Start by heating the olive oil and butter in a large skillet over medium heat. Once the butter has melted and the oil is hot, add the finely chopped onion. Sauté for about 4-5 minutes, or until the onion becomes soft and translucent. Then, toss in the minced garlic and cook for another minute, allowing the garlic to release its fragrance.

Add the sliced mushrooms to the pan. Cook them for about 5-7 minutes, stirring occasionally, until they release their moisture and start to brown. This step is key to developing the sauce's flavor and texture.

Once the mushrooms are nicely cooked, add the fresh thyme leaves and dried oregano. Stir them into the mushrooms and let the herbs infuse their flavor for another minute.

Pour in the dry sherry, using your spatula to scrape up any bits of mushroom or onion stuck to the bottom of the pan. This process is called deglazing, and it adds depth to the sauce. Let the sherry simmer for 2-3 minutes, allowing it to reduce by half.

Next, add the heavy cream and vegetable or chicken broth to the pan. Stir everything together and bring the sauce to a gentle simmer. Allow it to cook for another 5 minutes, stirring occasionally, until the sauce thickens to your desired consistency.

Taste your sauce and adjust the seasoning with salt and pepper. Once the sauce is ready, remove it from the heat and garnish with fresh parsley or thyme if you like. Serve immediately over your favorite dish!