Stir together mayonnaise and pesto sauce. (**Note: the pesto is a little salty--some might like it that way. However, I would suggest using between 1 and 2 tablespoons of pesto and see how you like it!).
Spread evenly on 1 side of each sourdough bread slice.
Place 4 bread slices, pesto sides down, on wax paper.
Layer 4 bread slices on wax paper each with 1 fontina cheese slice, bell peppers, and 1 Cheddar cheese slice; top with remaining bread slices, pesto sides up.
Cook sandwiches, in batches, on a hot griddle or in a nonstick skillet over medium heat, gently pressing with a spatula, 3 minutes on each side or until golden brown and cheese melts.
*Provolone or mozzarella cheese slices may be substituted.