In a 6qt soup pot or Dutch oven, over medium-high heat, cook the bacon until crispy, about 6-7 minutes. When ready, using a slotted spoon, transfer the bacon to a plate lined with paper towels to drain any excess grease.
Drain off some of the bacon fat, keeping about 2 tablespoons of the drippings in the pot to sauté the vegetables and aromatics. Lower the heat to medium heat.
Add the celery, onion and jalapeño and cook, stirring frequently until the vegetables become tender, about 5-6 minutes. Stir in the garlic and thyme and cook until aromatic, about 45 seconds.
Next, add the butter and stir until completely melted. Sprinkle the flour into the pot to make a roux. Stir until the flour is fully incorporated and cook, stirring constantly for about 2 minutes or until the roux begins to get lightly browned.
Gradually, add the beer, stirring until the mixture starts thickening, about 2-3 minutes. Add the chicken broth slowly, while stirring constantly then, add the half and half and mix to combine. Bring to a gentle bubble, lower the heat and simmer for about 3 minutes, stirring occasionally. Remove from the heat.
Gradually, sprinkle in the Gruyere and smoked cheddar cheese, mixing after each addition, until the cheese is fully melted. Next, gradually add the sharp cheddar cheese, mixing after each addition until the cheese melts.
Add half of the cooked bacon into the soup, reserving the remaining bacon to use as a topping. Season the creamy soup with salt and ground black pepper to taste.
Ladle the soup into bowls and garnish with crispy bacon, chopped chives and/or fresh thyme. Serve with toasted bread.