Gently dap the pineapple rings with a kitchen paper or cloth to absorb excess moisture and water. Cut each of the 4 pineapple rings into two to get 8 halves and set aside.
To assemble one grilled cheese sandwich, spread 1 1/2 tsp of mayonnaise on one side of a bread slice. Place the bread slice mayonnaise side down on a cutting board. Add 2 tbsp of tomato pasta sauce and spread evenly. Place 3 slices of white ham and add 4 halves of the pineapple rings (the configuration of placement is flexible as long as they fit in the sandwich). Add 3/4 cup of shredded mozzarella cheese and cover with a slice of bread. Gently press on the sandwich with a flat bottomed spatula.
Heat 1 tbsp of canola oil in a pan over medium heat. Place the grilled cheese sandwich, mayonnaise side down, on the pan. Gently press on the sandwich with a spatula to flatten it slightly and let cook for 3 minutes or until the bottom side is browned and crispy. Before turing the grilled cheese around, spread 1 1/2 tsp of mayonnaise on the top side of the sandwich. Turn the grilled cheese around and cook for another 3 minutes or until browned and crispy. Repeat steps 2 and 3 to make the other grilled cheese sandwich.