In a medium bowl, combine undrained tuna, chopped red onion, parsley, and mayo, flaking tuna as needed with a fork.
Spread tuna over one slice of sourdough bread (you probably won't be able to get all the tuna on the sandwich, that's ok, you can snack on the leftover tuna as you toast the sandwich). Top the tuna with sliced Havarti, and the last slice of bread.
Heat a grill pan over medium-low heat. Once hot, spray the pan with olive oil, and place tuna sandwich in the pan. Allow the sandwich to toast and grill marks to develop, approximately 5-10 minutes of cooking. Spray top of sandwich with olive oil, and gently flip sandwich to allow grill marks to develop on the other side. Continue to cook for another 5 minutes until both sides are golden brown and crispy.
Remove from pan and slice in half for serving. Enjoy immediately.