Melt the 3 tablespoons of unsalted butter in a large, heavy-bottomed stockpot or Dutch oven set over medium heat. Drop in the chopped yellow onion and celery, sautéing for 5 to 6 minutes while stirring frequently until the vegetables soften and become fragrant.
Pour the 3 cups of chicken broth directly into the pot, using a wooden spoon to scrape up any browned bits stuck to the bottom. Add the finely diced potatoes, garlic powder, dried thyme, and smoked paprika, stirring to distribute the spices uniformly.
Bring the liquid up to a rolling boil over medium-high heat, then immediately reduce the flame to medium-low. Leave the pot uncovered and simmer gently for 12 to 15 minutes, or until the potato cubes are completely fork-tender but not disintegrating.
Reduce the stove burner heat to low. Stir in the condensed cream of potato soup and condensed cream of celery soup, whisking gently until the thick soup bases dissolve smoothly into the warm broth baseline.
Add the cubed smoked ham, sweet corn kernels, and 2 cups of half-and-half straight into the pot. Stir carefully to integrate all the elements into a cohesive chowder matrix.
Let the chowder simmer gently on low heat for an additional 10 to 12 minutes, stirring occasionally to prevent the dairy sugars from scorching on the bottom of the pan. Do not let the soup come to a boil after adding the half-and-half, as intense bubbling heat can cause the dairy fats to break and curdle.
Remove the pot from the burner. Taste the velvety broth and adjust with salt and freshly cracked black pepper to your personal preference.
Ladle the hot, steaming chowder into deep bowls. If desired, scatter fresh chopped parsley and a handful of crispy crumbled bacon over the top of each serving to add a brilliant pop of color and texture.