Place the bacon into a large pot over medium-high heat. Cook until crisp, turning as needed. Crumble, and return to the pot.
Reduce the heat to medium, and add the onion, green pepper, red pepper, celery. and garlic. Cook and stir until the onion is transparent, and the peppers are soft. Add the crawfish, and cook until the liquid evaporates, and the crawfish begin to brown. Remove the contents of the pot, and set aside.
Pour the chicken broth into the pot, and add the potatoes. If the chicken broth does not cover the potatoes, add enough water to compensate. Bring to a boil, and cook for 8 to 10 minutes, or until the potatoes are soft. Add the carrots, and cook for about 8 more minutes.
Reduce the heat to low, and return the vegetables and crawfish to the pot. Stir in the half-and-half, and heat through. Do not boil. Season with salt and pepper to taste. Ladle into bowls and garnish with Cheddar cheese to serve.