Peel and mince the garlic. Gently crush the green peppercorns with the flat side of a knife to release their aroma.
In a medium saucepan, melt the butter with the olive oil over medium heat (the olive oil prevents the butter from burning). Add the minced garlic and sauté until fragrant, being careful not to brown it.
Add the crushed green peppercorns and sauté for another 1-2 minutes to allow the flavors to develop.
Pour in the beef broth and bring to a simmer. Reduce the heat to low and simmer for 5 minutes to allow the flavors to meld.
Stir in the heavy cream and mix well. Continue to simmer for 5-7 minutes, or until the sauce has thickened to your desired consistency.
Season with salt and freshly ground black pepper to taste. Stir well and let it simmer for another minute.
Serve immediately over grilled meats, steak, or store in an airtight container in the refrigerator.
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