Slice each pepper lengthwise in half, and discard seeds and membranes (use a spoon to scrape them out). Wearing gloves is recommended to protect your hands from capsaicin, which is mainly in the seeds and membranes.
In a microwave-safe mixing bowl, add cream cheese. Microwave until softened, 15 to 30 seconds. The cream cheese should be very soft to the touch so that it can be easily stirred with other ingredients. Add cheddar cheese and garlic powder, stirring with the cream cheese until well-mixed.
Stuff each pepper half with the cream cheese mixture. Wrap a halved bacon slice around each pepper. Secure with a toothpick, as needed. Place the stuffed pepper halves in a single layer on a baking tray, optionally lined with foil for easier cleanup.
Bake at 400 F until the cheese is starting to brown on top, 20 to 25 minutes. Optionally, turn on the broiler and broil for a few minutes to crisp up the bacon. Remove from the oven and let cool for 5 minutes before serving. Don't wait too long before eating because they are fantastic when hot and they can cool rapidly.