Cook the bacon in a large soup pot set over medium heat until rendered and crispy, about 5 – 7 minutes. Remove with a slotted spoon to a paper towel-lined plate to drain. If the bacon has rendered a lot of fat, remove all but a few tablespoons from the pot before continuing.
Add the white onion, celery, and jalapeño to the bacon drippings along with a sprinkling of kosher salt and cook, stirring occasionally, for about 3 minutes, or until vegetables have softened and become translucent.
Stir in the garlic and cook until fragrant, about 1 minute more.
Add the potatoes and sweet corn to the pot, followed by the bay leaf, paprika, and cayenne pepper, if using. Season with kosher salt and pepper to taste.
Pour chicken stock into the pot, stirring everything together and making sure there is enough liquid to cover all the ingredients.
Cover and bring soup to a boil, then reduce to a simmer. Cook until potatoes are tender, about 10 – 15 minutes.
Using a slotted spoon, remove about half of the vegetables from the liquid and set aside in a mixing bowl. Be sure to also remove the bay leaf and discard.
Using an immersion blender, puree the remaining vegetables with the liquid to a smooth chowder base. (This can also be done by transferring the remaining vegetables and liquid to a blender and very carefully blending – always use caution when blending hot liquids.)
Return reserved vegetables to the pot and stir in heavy cream. Taste the chowder, adjust seasoning, and serve with the reserved crispy bacon pieces and fresh parsley, scallions, or chives.