In a small bowl, whisk together the mustard and mayonnaise to create the Dijonnaise. Spread on one side of each slice of bread.
Add the butter to a medium nonstick skillet and melt over medium heat. Add the bread slices (you should hear them sizzle when they hit the pan) and grill until browned, about 2 minutes. Flip over and brown the opposite sides, 1 to 1 1/2 minutes longer (the second side usually browns more quickly than the first).
Top each slice with cheese, and heat until the cheese starts to melt. Add the kale leaves, tomato, and avocado slices and top with a slice of bread. Once the cheese has fully melted, remove the pan from the heat.
Transfer the sandwiches to a cutting board and let them cool for 2 minutes before slicing. Cut into two diagonal pieces and serve immediately. Season with sea salt, if desired, pair with a glass of almond milk and a smile!