Start by heating the olive oil or butter in a medium saucepan over medium heat. Once heated, sauté the finely chopped onion and minced garlic until they become translucent and aromatic.

Add the chopped dark sweet cherries to the saucepan, stirring frequently until the cherries start to break down and release their juices, approximately 5 minutes.

To the cherry mixture, blend in ketchup, apple cider vinegar, brown sugar, and honey. Stir thoroughly to ensure the ingredients are well mixed.

Sprinkle smoked paprika, ground mustard, black pepper, and cayenne pepper (if using) into the sauce. Mix these spices well into the sauce base to distribute flavors evenly.

Reduce the heat to low and allow the sauce to simmer gently. Stir occasionally, and let it cook for about 20 minutes, or until the sauce reaches a thick, rich consistency.

Taste and adjust the seasoning with salt, and additional spices if needed. For a thinner consistency, a bit of water can be added.

For a smoother texture, use an immersion blender to puree the sauce right in the pan until it reaches your desired smoothness. Alternatively, carefully transfer to a blender, puree, and then return to the pan.