Lay down 4 slices of sourdough bread; spread each with garlic aioli.
Layer black forest ham, cheddar cheese, arugula, and red onion evenly over the 4 slices; top with other bread slices.
Preheat a griddle on medium-high heat; add olive oil and heat until shimmering (2 min).
Place all sandwiches on oiled griddle at once; allow to heat a few minutes until surface is golden brown; turn sandwiches over and repeat process on other side; serve warm.