For the vinaigrette: Heat a cast-iron skillet over medium-high heat. Add 2 teaspoons of the olive oil and 1 tablespoon of the honey. When the honey has melted, stir it together with the oil. Place the lemons, cut-side down, into the honey mixture; cook until the lemons look charred and the honey has caramelized, 2 to 3 minutes. Remove the lemons to a baking sheet and let cool. Set the skillet aside.
Juice the roasted lemons and add 1/4 cup of the juice to a bowl; whisk in the remaining 1 teaspoon honey and the mustard. Once combined, whisk in the remaining 2 tablespoons olive oil until the dressing becomes emulsified. Season to taste with salt and pepper. Refrigerate until ready to serve.
For the salad: Return the skillet to high heat. When hot, add the cherry tomatoes and season with salt. Cook until the caramelized honey coats the tomatoes and the tomatoes just begin to char, 1 to 2 minutes. Remove the skillet from the heat.
Combine the escarole, Treviso, almonds, basil and mint in a large bowl; season with salt and pepper. Toss the salad with the dressing, and then gently fold in the charred tomatoes. Transfer the salad to the serving platter and, using a peeler, shave Parmesan over the top.