Heat your panini grill or grill pan according to the manufacturer’s directions.
Assemble the sandwich: 1 slice of bread, prosciutto, fontina, spinach, slow-roasted tomatoes, and the other slice of bread. Brush one side with olive oil.
Place sandwich on the grill, oiled side down, and brush more olive oil on the top. Close the grill top and grill for 2 to 3 minutes, until the cheese sizzles. Remove and allow to cool for a minute or two before cutting. (If using a grill pan, grill the sandwich oiled side down and brush more olive oil on top. Grill for 2 to 3 minutes, then flip and grill another 2 to 3 minutes. You can also use press the sandwich with the bottom of a cast iron skillet or a sandwich/bacon press.)