¾ cup crème fraîche or sour cream
About 1/4 cup prepared horseradish
¼ cup finely chopped fresh chives
2 tbsp. Worcestershire sauce
1 tbsp. coarsely ground black pepper
3 tbsp. butter
1 large white onion, sliced Salt
4 brioche burger buns, split
About 2 tbsp. canola, safflower, or peanut oil
1 ¼ to 1 1/2 lb. very thinly sliced boneless rib eye (look for beef sliced for Philly cheesesteaks, a.k.a. top round steak, in the packaged meat section; or in a pinch, use very thinly sliced rare deli roast beef)
Bread-and-butter pickle slices
8 oz. extra-sharp white cheddar, coarsely grated
2 cups watercress or upland cress, leaves and tender sprigs only
Preheat the broiler. In a medium bowl, stir all the sauce ingredients until blended.
In a medium skillet, melt 1 tbsp. butter over medium-low to medium heat. Add the onion; season with salt. Cook, stirring often, until the onion is softened, about 10 minutes. Add 1/2 cup water. Cook, stirring occasionally, until the water evaporates, about 5 minutes. Remove the onion from heat.
In a small bowl, microwave the remaining 2 tbsp. butter on high until melted, 30 to 40 seconds.
Toast the buns under the broiler until golden brown, 1 to 3 minutes. Brush the cut sides of the buns with the melted butter.
Heat a large griddle or cast-iron skillet over medium-high to high. Add a drizzle of the oil. Working in batches, add the beef in a single layer; season with salt, pepper, and granulated garlic. Using tongs to turn the beef, cook until browned and crisp, 1 to 2 minutes per batch; add more oil between batches. Transfer the beef to a platter; tent with foil to keep warm.
Divide the onion among the bun bottoms. Top each with some pickles, a few slices of warm beef, some sauce, and the grated cheese. Repeat the layering 2 more times with the beef, sauce, and cheese. Top with some cress and more sauce. Set the bun tops in place.