Begin by cooking your bacon in a skillet over medium heat until it’s crispy and golden. Drain on paper towels and set aside. You can do this ahead of time if you like—it reheats well.
In a small blender or food processor, combine the crumbled feta cheese and cream cheese. Blend until the mixture is smooth, fluffy, and spreadable. This should take about 30 seconds. If it’s too thick, add a teaspoon of water or milk to loosen.
In a small skillet, melt the butter over medium-low heat. Add the minced garlic and sauté for about 1–2 minutes, just until fragrant and lightly golden. Be careful not to let it brown too much. Turn off the heat and set aside.
Heat a large skillet (preferably cast iron) over medium-high heat until hot. Place the beef balls in the skillet and immediately press down each one with a flat spatula to form a thin patty. Let them cook undisturbed for 2–3 minutes until a dark crust forms. Flip and cook the other side for another 2–3 minutes. Remove from the skillet and let rest briefly.
Toast the burger buns in a dry skillet or toaster until lightly golden. While still warm, brush the cut sides generously with the garlic butter mixture.
Spread a generous layer of whipped feta onto the bottom bun. Place a hot smashed patty on top, add a slice of crispy bacon, and close with the garlic-buttered top bun. Serve immediately while everything is warm and melty.