Cut the kernels off the corn cobs; set kernels aside. Place the stripped cobs in a large pot with the chicken broth and milk. Bring to a boil, then reduce heat and simmer uncovered for 15 minutes. Remove and discard the cobs with tongs.
In a large Dutch oven over medium heat, cook the diced bacon until crisp, 6–8 minutes. Remove with a slotted spoon to a plate, leaving the fat in the pot.
Add 1 tablespoon of the butter to the pot. Add the onion, celery, and carrot; cook, stirring occasionally, until softened and translucent, about 7–8 minutes. Stir in the garlic and cook 1 minute more.
Add the remaining 2 tablespoons butter. Once melted, sprinkle in the flour and stir constantly for about 1 minute, until pale gold.
Slowly whisk in the corn stock until smooth. Add the potatoes, corn kernels, thyme, bay leaf, salt, pepper, and cayenne. Bring to a light boil, then reduce heat and simmer uncovered 15–18 minutes, until the potatoes are tender.
Remove the bay leaf. Take the pot off the heat and let it sit for a minute, then stir in the heavy cream and most of the bacon.
Taste and adjust salt and pepper. Ladle into bowls and top with remaining bacon and chives.
