Cut each piece of bacon into bacon strip into 3 equal pieces. Place in a single layer between 2-3 sheets of paper towels and microwave on a microwave-safe plate for 2-3 minutes per batch. The bacon will be partially cooked, rendered and flexible at this point.
Mix softened cream cheese and shredded cheese. Fit into each hollowed out jalapeno half.
Wrap each piece of bacon around the jalapeno halves, securing with toothpicks. Bake for 15-20 minutes until the cheese has melted and the bacon crisps. Allow to cool on pan for 5 minutes. Serve each with a big dollop of sour cream.