In a small bowl, combine mayonnaise, lemon juice, and pepper, whisking well. Cover, and refrigerate until ready to use.
Using a 2¼-inch square cutter, cut 32 squares from bread slices.
Spread 1 side of each bread square with ½ teaspoon mayonnaise mixture.
Trim turkey and cheese slices to fit bread squares, and place between 2 bread slices, mayonnaise sides to the inside. Spread outside of each bread slice with butter.
Heat a nonstick griddle over medium-high heat.
Grill each sandwich, pressing down lightly with a spatula to flatten slightly. Cook until golden brown, approximately 3 minutes per side.
Top each sandwich with a cherry tomato slice and a sprig of dill.
Serve immediately.
Recipe by TeaTime Magazine at https://teatimemagazine.com/mini-dill-havarti-and-turkey-paninis-recipe/