In a medium bowl, combine the ground turkey, garlic powder, onion powder, sea salt, and black pepper until well incorporated.
Form the turkey mixture into a single patty that roughly matches the shape and size of your sourdough slice.
Heat the avocado oil in a cast-iron skillet or non-stick pan over medium-high heat until shimmering.
Place the turkey patty in the skillet and sear for 5 to 6 minutes on the first side until a golden-brown crust forms.
Flip the patty and cook for another 4 to 5 minutes, or until the internal temperature reaches 165 degrees Fahrenheit.
During the last minute of cooking, place the white cheddar cheese on top of the patty and cover the pan with a lid to melt.
While the cheese melts, toast the sourdough bread slice until it is golden and crisp on both sides.
Spread the Dijon mustard evenly across the toasted sourdough.
Place the cheesy turkey patty onto the toast and top with a generous handful of fresh arugula before serving.