In a large skillet over medium-high heat, warm the oil.
Sprinkle the beef with 1/2 teaspoon each salt and pepper. Add the beef to the hot skillet, browning it evenly, 5 to 6 minutes. Transfer it to a paper towel–lined plate. Reduce the heat to medium.
Carefully wipe any residual liquid from the skillet. Add the butter and garlic cloves, and sauté until browned and fragrant, 4 to 6 minutes. Splash in 2 cups of the broth, the thyme, and rosemary. Simmer over low heat for 25 minutes, stirring occasionally.
In a small bowl, whisk together the flour and cream until a paste forms. Pour in the remaining 1/2 cup broth, whisking until smooth.
Return the beef to the skillet with the garlic and toss until heated through. Remove the skillet from the heat, pour the cream sauce into the hot skillet, and stir to combine. Let the sauce thicken, about 1 minute. Season to taste with salt and pepper.
Serve over cooked rice, potatoes, or pasta.