Cut the potatoes in halves or quarters so they are uniform in size. Add the cut potatoes to a large pot of salted boiling water. Boil the potatoes about 8-10 minutes or until barely fork tender.
Drain the potatoes well, and transfer to a large baking sheet in a thin even layer. Toss potatoes in a very light dusting of all-purpose flour (about ½ - 1 tablespoon). *I like to use a fine mesh strainer for this so that I don’t add too much flour. This step is key for crisp texture on the griddle.
Heat griddle on medium heat. Then add about 2-3 tablespoons high-heat cooking oil (or tallow or bacon grease) to the heated surface and spread it around with your spatula.
Place the potatoes cut side down on the oiled surface, and allow them to cook untouched for about 6-8 minutes for a nice charred golden color to develop. *If adding the chopped onions, add those to the griddle as well, nestling them in between the potatoes.
While the potatoes cook, begin making the cowboy butter in a skillet over medium heat. Add a stick of butter to a large skillet with garlic and shallot. Sauté until the garlic and shallot are softened, but not browned. Then add the crushed red pepper flakes. Continue to cook until the butter is fully melted.
Remove the butter from the heat and add the remaining cowboy butter ingredients to the skillet, including the Dijon mustard, Worcestershire sauce, smoked paprika, all-purpose seasoning, horseradish, and lemon juice. Mix thoroughly, taste, and adjust the seasoning if needed.
Once a golden brown color develops on the bottom of the potatoes, begin to sauté together the potatoes and onions. Continue to cook until the potatoes are done to your liking. *Total cooking time for potatoes could be 15-18 minutes, depending on your griddle's heating capabilities.
When potatoes are deeply golden and cooked through, transfer them (along with onions) to a large bowl. Pour the cowboy butter over the hot potatoes, sprinkle with freshly chopped chives and parsley, and toss well.
Let the potatoes rest about 3-4 minutes, then serve. Sprinkle with more chives or parsley for garnish. *As you’re serving the potatoes, be sure to scoop from the bottom of the bowl. All of that concentrated cowboy butter seeps down through the cracks, so you’ll need to redistribute it as you plate the potatoes