Place 1 to 2 slices of fontina atop 1 bread slice. Top with the onions. Season with salt and pepper. Then add spinach and prosciutto. Add the remaining slice(s) of fontina. Top with the second bread slice. Brush both sides of the sandwich with the oil.
Heat a grill pan over medium-low heat. Grill the sandwich until the bread is golden brown and the cheese melts, pressing down with a metal spatula or grill press, about 4 minutes per side.