In a mixing bowl, combine the softened butter, chopped basil, minced garlic, lemon zest, and lemon juice. Mix well until all ingredients are fully incorporated. Place the compound butter on a sheet of plastic wrap, shape it into a log, and refrigerate until firm.

In a skillet over medium heat, add a splash of olive oil. Add the sliced shallots and sauté until they become golden brown and crispy, about 10-15 minutes. Remove from heat and set aside.

Pat the ribeye steaks dry with paper towels. Rub both sides of the steaks with olive oil and season generously with kosher salt and cracked black pepper.

Preheat a grill or cast-iron skillet over high heat. Add the seasoned ribeye steaks to the hot grill or skillet. Cook for about 4-5 minutes on each side for medium-rare, or until desired doneness is achieved. Use a meat thermometer for precise cooking (130°F for medium-rare).

Once cooked, remove the steaks from the heat and let them rest for 5-10 minutes. This allows the juices to redistribute.

Top each ribeye with a generous slice of the basil-infused compound butter and a sprinkle of crispy shallots. Serve immediately with your choice of sides.