In a 4.5-quart soup pot, slowly cook the extra-thick bacon strips over low heat. (I find cutting the bacon in half helps it fit better and cook evenly.) As the bacon cooks, prepare and measure out the other ingredients. Once the bacon is crisp, transfer it to a paper towel-lined plate to drain. Once cooled, chop the bacon into bite-sized pieces. Reserve 2 tablespoons of bacon fat from the pot, and wipe out any dark burnt spots, but leave the flavorful browned bits for added depth in the soup.
Season both sides of the chicken breasts or thighs with a generous amount of salt and pepper. Heat 1–2 teaspoons of olive oil in the pot (or add 2 tablespoons of unsalted butter if not using bacon fat) over medium-high heat. Sear the seasoned chicken for about 3 minutes per side until a golden crust forms. It’s okay if the inside is still undercooked, as it will finish cooking in the soup. Remove the chicken from the pot and let it rest for 10 minutes before cutting it into bite-sized cubes. I always let the chicken rest before cutting to keep it juicy and tender.
Return the reserved bacon fat to the pot over medium heat. Use a silicone spatula to scrape and dissolve any browned bits from the bottom and sides for extra flavor. Add the diced onions, carrots, and celery, tossing to coat in the fat. Sauté for about 5 minutes until softened. Mix in the minced garlic, hot sauce, Worcestershire sauce, dried parsley, dried rosemary, dried oregano, mustard powder, black pepper, and crushed red pepper flakes. Stir well to combine and allow the spices to become fragrant.
Sprinkle the flour over the vegetable mixture, stirring to evenly coat, and cook for about 2 minutes to remove the raw flour flavor. Gradually pour in the chicken broth in small splashes, stirring continuously and scraping up any browned bits as you go. Slowly add the half & half in the same manner to ensure a smooth soup base. Peel and dice the potatoes into bite-sized pieces, then add them to the pot. Bring the soup to a boil, then reduce to a gentle simmer. Return the cubed chicken (from Step 2) and any accumulated juices to the pot. Partially cover and simmer over medium heat for about 20 minutes, or until the potatoes are fork tender.
Reduce the heat to low. Stir in the shredded cheddar cheese a little at a time until melted and soup is creamy. Add half of the chopped bacon (from Step 1) into the soup, reserving the remaining bacon for garnish. Ladle the soup into bowls and top each serving with the reserved bacon and a generous sprinkle of sliced green onions. For a little extra zing, I like to add an extra dash of hot sauce before serving.