In a large skillet, with a splash of oil or fat, roast pine nuts on medium heat, being sure to constantly stir so as not to burn. This should only take 3 minutes or so. Let cool off burner.
In a food processor add cooled pine nuts, lemon juice, garlic cloves, and sea salt. Pulse until well chopped.
Add the basil and shredded Parmesan and pulse again until smooth.
Drizzle in the olive oil, a bit at a time while food processor is running, making sure the pesto is well blended.
Slice Swiss cheese thickly and heat skillet over medium heat with butter added to the pan and make sure the melted butter is covering entire pan.
Assemble the bread with pesto first, spread evenly, and cheese on top. Cover with other slice and place in the heated pan, flipping one or twice until the cheese is melted and the toast is a golden brown. Be attentive to the grilling process, as it's easy to burn.
Lower heat if necessary to finish the others. Add more butter in between sandwiches and make sure all bread surfaces have enough butter to grill.
When grilled cheese sandwiches are done, plate and serve hot with salt and pepper, to season.