Prepare the steaks. Trim excess fat and silver skin if needed. Rub the steaks lightly with oil and season generously with kosher salt and freshly cracked black pepper. For deeper flavor, wrap and refrigerate for a few hours. Remove from the refrigerator about 30 minutes before cooking.
Make the cowboy butter. Melt the butter in a small saucepan over low heat. Whisk in the lemon juice and zest, garlic, Dijon mustard, paprika, cayenne, dried thyme and red pepper flakes. Remove from the heat and stir in the chives and parsley. Season with salt and pepper. If the lemon causes the sauce to separate, whisk in 1–2 tablespoons room-temperature butter, a little at a time, until smooth and emulsified. Divide the cowboy butter in half, reserving one half for the slider buns and the other half for tossing with the steak.
Caramelize the onions. Heat a large skillet over medium heat and add a few tablespoons of butter. Add the sliced onions and cook for approximately 15–20 minutes, stirring occasionally, until soft, golden brown and caramelized. Reduce the heat if needed to prevent burning. Transfer the onions to a bowl and set aside.
Sear the steaks. Increase the skillet heat to medium-high and add 1–2 tablespoons avocado oil. Pat the steaks dry and place them in the hot skillet without overcrowding. Sear for approximately 3–4 minutes per side, or until a deep golden crust develops and the steaks reach your desired doneness. Adjust the cooking time based on steak thickness.
Rest and slice. Transfer the steaks to a cutting board and loosely tent with foil. Rest for 10 minutes, then slice thinly against the grain.
Coat with cowboy butter. Reduce the skillet heat to low. Return the sliced steak to the pan and pour in half of the prepared cowboy butter. Toss gently until every piece is coated in the garlic-herb butter sauce. Remove from the heat.
Prepare the slider buns. Preheat the oven to broil. Arrange the split slider buns, cut sides up, on a foil-lined baking sheet. Brush the inside of the buns with the reserved half of the cowboy butter and add Havarti cheese to both the top and bottom buns.
Assemble the sliders. Divide the caramelized onions among the bottom buns, then layer the cowboy butter-coated steak over the onions.
Broil until melty. Broil for 1–2 minutes, watching closely, until the Havarti melts and the bun edges are lightly golden.
Finish with cowboy butter. Place the top buns over the steak and brush the tops with any remaining cowboy butter from the skillet. Separate into individual sliders and serve warm.