Combine the butter and olive oil in a saucepan over medium-low heat.
Once the butter has just melted, add the garlic and cook for 2 - 3 minutes, until the garlic is fragrant.
Sprinkle the flour into the pan, and whisk to form a paste.
Cook the flour mixture (called a roux) for another 2 - 3 minutes, until it turns a golden brown color.
Gradually add the broth to the pan, whisking continuously to incorporate the liquid and break up any lumps.
Increase the heat to medium-high, and continue whisking until the mixture comes to a boil (4 - 5 minutes).
You will notice that the sauce will start to thicken. Reduce the heat to low and stir in the tomato sauce and spices.
Continue to simmer for about 10 - 15 minutes, stirring occasionally. The sauce should be thick and smooth.
Remove from the heat, taste, and adjust the seasonings. Season with salt and pepper to taste.