Preheat Blackstone griddle to medium heat. Drizzle vegetable oil then add the sliced onions. Cook for 5 minutes until tender.
Add the deli turkey to the griddle, lightly chop with spatulas and mix with the onions until lightly seared. Divide the turkey mix into 4 equal portions and top each one with 2 slices of Swiss cheese. Cover with the griddle’s hood or a basting dome for 2 minutes until the cheese is melted.
Lay the bread out onto the griddle and toast on one side for 3 minutes. Spread the pesto onto the untoasted side of the bread.
Use spatulas to set the turkey and cheese onto the bread, layer the tomatoes, then top with the other slice of bread. Remove from the griddle, cut in half, and serve immediately.