Combine chopped turkey ham and mayonnaise in a small bowl and set aside.

Dice or coarsely chop fresh pineapple; if using fresh pineapple, toss with sugar to taste in a separate bowl.

Lay out bread slices. Spread pineapple on 4 slices.

On the remaining 4 bread slices, layer pickles, turkey ham salad mixture, sliced onion, and Taleggio cheese.

Carefully top the ham and cheese slices with the pineapple-topped bread slices to form sandwiches; press together tightly.

Brush each side of the sandwiches lightly with olive oil.

Heat a heavy nonstick skillet or panini press over medium-high heat.

Place the sandwiches in the pan, browning and pressing until the first side is crisp and golden, and the cheese begins to melt.

Turn sandwiches and cook the second side, pressing as they brown.

Once the sandwiches are crisp and lightly browned on both sides, and the cheese is melted, remove from the pan.

Cut the sandwiches in halves and serve immediately.