Cut the kernels off the corn cobs by standing each cob upright in a wide bowl and carefully slicing downward. After removing the kernels, scrape the cobs with the back of your knife to extract the sweet corn "milk". Reserve 1 cup of corn kernels for adding texture later.
Melt butter in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced onion, carrots, and celery, sautéing for 5-7 minutes until softened but not browned.
Add the diced bell pepper and minced garlic, cooking for another 2 minutes until fragrant.
Stir in most of the corn kernels (remember to reserve that 1 cup!), potatoes, thyme sprigs, and bay leaf. Season with ½ teaspoon salt and ¼ teaspoon pepper.
Add the broth and bring to a simmer. Reduce heat to medium-low, cover partially, and cook for about 15-20 minutes until the potatoes are fork-tender.
In a small bowl, whisk together the half-and-half and flour to create a slurry. Slowly pour this mixture into the soup, stirring constantly. Simmer for another 5 minutes until the chowder thickens slightly.
Add the reserved cup of corn kernels and cook for just 3 minutes more. Remove the thyme sprigs and bay leaf before serving. Garnish with fresh chives or green onions.