In a medium skillet, heat the olive oil over medium high heat. Toss in the garlic, and cook for 1 or 2 minutes. Add the greens, 1/4 teaspoon salt, pepper, and red pepper. Sauté for 3 minutes, moving the greens around a bit so they don't scorch. Flip the greens and continue to cook until tender. Finish with the splash of vinegar. Remove to a plate.
In the same skillet, melt the butter over medium heat. Add the eggs and the remaining 1/4 teaspoon of salt, or more to taste. Cook for 3 minutes, use a spatula to gently move the eggs so the bottom doesn't stick, cover, and continue to cook until the whites are set. Carefully set on top of the greens, and serve immediately.