Preheat the oven to 400 degrees F. Grease 12 muffin tins. For muffins: In a mixing bowl, combine the flour, sugar, baking powder and apricots together. In a separate bowl, mix the egg, cream, rum and oil together. Fold the flour mixture into the egg mixture just enough to moisten the dry ingredients. Muffins must not be overmixed. If overmixed, the muffins will be tough. The batter should be lumpy and not smooth. Spoon the mixture into the prepared tins. Bake for 20 minutes.
For the butter: In a mixing bowl, combine all the ingredients together and mix until incorporated. Using a 8 by 10-inch piece of plastic wrap, spoon the butter onto the center of the wrap. Fold the wrap over and roll the plastic up, forming a log shape. Refrigerate until the butter has set, about 10 minutes. Remove the muffins from the oven. Remove the butter from the refrigerator and unwrap. In a napkin-lined basket, invert the muffins into the basket. Place the spiced butter on a small dish and set to the side of the basket.
Yield: 12 muffins