Preheat oven to 400 degrees. In a 6-8-oz baking ramekin, swirl 2 tsp. melted better to coat. Add 2 tsp. heavy cream. Crack both eggs, being careful not to break yolks. Sprinkle in salt and pepper. Sprinkle in cheese, and top with dill.
Place in oven for approximately 12-14 minutes or until eggs are just barely set. Allow to cool for 5 minutes before service--the dish and eggs will still be very hot.
For sauce (serves 4-6): roast red pepper until completely black over open flame on grill or gas stove (you may also place under a broiler in the oven). Allow to cool for 5-10 minutes and remove blackened peel under slowly running cool water. Rough chop pepper and saute in 2 tsp. butter in a small skillet for 5 minutes over medium heat.
Add chardonnay and reduce heat to medium low. Allow chardonnay to reduce to 1 Tablespoon. Place pepper mixture in food processor or blender. Add salt and 1/4 cup heavy cream and puree until smooth.
Gently reheat on stovetop over low heat. Do not allow to boil. Serve warm sauce over baked eggs and serve immediately.