In a large Dutch oven or heavy pot over medium heat, cook the chopped bacon until crisp, 8 to 10 minutes. Use a slotted spoon to remove the bacon and set it aside, leaving about 1 tablespoon of rendered fat in the pot.
Add the diced onion, celery, and carrot to the pot. Cook for 7 to 8 minutes, stirring occasionally, until the vegetables begin to soften.
Stir in 1 to 2 tablespoons of the reserved sun-dried tomato oil. Cook for about 30 seconds, just until warmed.
Add the chopped sun-dried tomatoes and cook for 2 to 3 minutes, stirring occasionally, until they soften and release their flavor.
Stir in the garlic and cook for about 30 seconds.
Add the potatoes, corn (whole kernel and creamed), salt, pepper, cayenne, and paprika.
Pour in the chicken broth, milk, and heavy cream. Stir well to combine.
Bring the mixture to a gentle simmer, then reduce heat to low. Cook uncovered for 15 to 20 minutes, or until the potatoes are tender.
Remove 2 cups of the soup and blend until smooth, then stir it back into the pot.
Return most of the cooked bacon to the chowder and stir to combine. Taste and adjust seasoning as needed.
Ladle into bowls and top with remaining bacon. Finish with chopped chives or parsley and a few extra bits of sun-dried tomato, if desired.