Drain the tuna very well and transfer to a medium bowl. Press it firmly in the strainer or pat dry with paper towels to remove as much moisture as possible. Add the Greek yogurt, Kewpie mayo, Dijon mustard, and finely minced Calabrian chili. Stir until the tuna is evenly coated and the base is smooth and creamy.

Add the chopped gherkin pickles, diced red onion, and fresh basil. Fold everything together until evenly combined. Taste and adjust salt, Dijon, and Calabrian chili as needed. The salad should be creamy, tangy, and have a gentle building heat from the chili.

Lay both slices of sourdough on a clean surface. Pile the tuna salad generously onto one slice spreading it all the way to the edges. Scatter the shredded cheddar evenly over the tuna salad. Place the second slice of bread on top and press down gently. Let the assembled sandwich sit for one minute before toasting so the filling settles.

Heat a generous drizzle of olive oil in a skillet over medium low heat. Place the sandwich in the pan and cover with a lid. Cook for 3 to 4 minutes until the bottom slice is deeply golden and crispy. Carefully flip the sandwich and replace the lid. Cook for another 2 to 3 minutes until the second side is equally golden and the cheddar is fully melted. Keep the heat on medium low throughout. Too high and the bread burns before the cheese melts.

Remove from the pan and let rest for one minute before slicing in half. Serve immediately while the bread is still crispy and the cheese is still melted and gooey.