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Step 1
Peel your potatoes and rinse in cold water. Place the potatoes in a large pot and add water to cover (around 10 cups) and ⅓ cup of the salt. Bring to a boil over high heat and cook the potatoes, uncovered, until just tender but with some bite still, 18 to 25 minutes. Be sure not to overcook the potatoes—you don’t want mushy potato salad! Drain the potatoes and transfer to a large bowl. Sprinkle with 1 teaspoon of the salt and allow to cool for 30 minutes or so.
Step 2
Meanwhile, in a large skillet, cook the bacon (if using) over medium heat until the fat is rendered and the bacon is crisp and browned, 7 to 10 minutes. Transfer to a paper towel–lined plate, leaving the fat in the pan. (If you’re omitting the bacon, melt the butter in a large skillet here.) Add the onion and fennel to the hot bacon fat in the skillet and cook until softened, about 5 minutes. Season with the remaining 1 teaspoon of salt. Remove from the heat and allow to cool.
Step 3
Add the cooled fennel mixture to the bowl with the potatoes, then add the olive oil, sour cream, chopped parsley, ground mustard, paprika, lemon zest, pickled banana pepper brine, and pepper and stir to combine. Taste! Taste! If necessary, you may need to add a tad more of the seasonings and sour cream. Garnish with the parsley leaves and, if desired, an extra pinch of paprika.
Step 4
We’re talking about potato salad here, so: everyone has their way. Some people make it the day of; some people make it the day ahead. Store in the refrigerator until ready to serve.