Soften the butter and spread on one side of each slice of bread. Spread the inside slices of bread evenly with pesto. Put a slice of Havarti on the bottom piece of bread, add artichoke hearts, and top with another slice of Havarti. Place the other piece of bread on top, creating a sandwich.
Heat a large skillet or griddle pan over medium-low heat and place the sandwiches butter side down. Cook for 4-5 minutes, or until the cheese starts to melt and the bread is golden brown. Carefully flip the sandwich over and cook for an additional about 3-4 minutes. Remove from heat and sprinkle with sea salt. Cut sandwiches in half and serve immediately.
