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Spread softened butter on the outside of each bread slice.
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In a food processor, add basil, 1/4 C olive oil, 1 t salt, 1 T parmesan cheese; blend.
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In a small bowl, mix mayo, lemon juice and Sriracha chili. You may want to add more than 1 teaspoon.
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Depending on heat, add to desired taste.
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Heat a cast iron pan to medium heat or use a sandwich press. if using the pan, use 1 T olive oil and then put buttered side of sandwich down. The oil and butter make a tastier mixture.
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Put one buttered side of bread down; spread with pesto mixture; add 2 slices Swiss and two slices fontina cheese, add onion slice and top with arugula.
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Spread other slice of bread with hot mayo. Put the mayo side inside.
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Cook approximately 2 minutes until browned on each side. Make sure cheese is melted and bread is nicely golden. Serve with more pesto for dipping, if desired.