Thinly slice the yellow onion into uniform half-moons.
Heat half of the olive oil in a skillet over medium-low heat and add the onions with a small pinch of the sea salt.
Cook the onions for 15 to 20 minutes, stirring occasionally, until they are soft and develop a deep golden brown color.
While the onions caramelize, divide the ground beef into two equal portions and gently form them into patties about one inch thick.
Season both sides of the beef patties evenly with the remaining sea salt, black pepper, and garlic powder.
Remove the caramelized onions from the skillet and set them aside on a plate.
Increase the skillet heat to medium-high and add the remaining olive oil.
Place the patties in the hot skillet and sear for 4 to 5 minutes per side until a savory crust forms and the internal temperature reaches your preference.
Toss the fresh arugula with the lemon juice in a small bowl to lightly coat the leaves.
Arrange the dressed arugula on a plate, place the seared patties on top, and crown them with the warm caramelized onions.