Brush one side of each slice of bread with olive oil (using all 3 Tablespoons of oil). Place each slice of bread oil side down.
On one slice of bread, add half of the mozzarella, half feta (slightly crumbled), half tomatoes and half arugula. Cover with a slice of bread. Repeat to create the second sandwich.
Heat a skillet (non-stick or cast iron) to medium heat. Add sandwiches and cook on one side until golden brown (about 4-5 minutes). Flip and cook 2nd side until golden brown. Eat immediately!