Assemble the Panini: Spread one slice of bread evenly with 2 tablespoons of the kale pesto. Layer half the tomato slices over the pesto, followed by half of the fresh mozzarella. Top with the second slice of bread. Repeat with the second panini.
Cook the Panini: Add the olive oil to a skillet over medium heat. When hot, place the 2 panini in the skillet. Reduce the heat to medium-low, cover the pan, and cook for 3–4 minutes, until the bread begins to turn golden brown.
Flip and Finish: Carefully flip the panini and cook, covered, for another 2–3 minutes on the other side, until golden and the cheese has softened.
Serve: Remove from the skillet, cut each panino in half, and enjoy immediately.