Lay the tomatoes on a small baking sheet and drizzle with avocado oil. Add a pinch of salt. Roast for 10-12 minutes until softened and lightly charred. Remove and let cool.
Put the tuna in a bowl with a generous pinch of salt and pepper. Chop the cooled tomatoes and add them to the tuna. Mix well.
Heat a large skillet over medium low heat. Add a tablespoon of butter. When it melts, add two slices of bread. Add 1/4 of the cheese to each slice, then add half of the tuna mixture. Divide the remaining cheese between the two sandwiches, then add the other two slices bread. Press down slightly.
Cover the pan and allow to cook for several minutes, being careful not to let your heat get too high. Check the sandwiches to see if the cheese is melted, and carefully flip. Continue cooking until both sides are golden brown.