Whisk together the Parmesan, lemon juice, 3 tablespoons olive oil and 1/2 teaspoon salt in a medium bowl. Set aside.
Preheat the oven to 375 degrees F. Heat a grill or grill pan to high.
On a rimmed baking sheet, toss the tomatoes with 1 tablespoon olive oil, 1/3 teaspoon salt and the red pepper flakes. Transfer to the oven and roast until golden brown and wrinkled, about 30 minutes. Let cool.
Meanwhile, place the curly kale leaves directly on the hot grill. Grill for about 1 minute per side, until wilted and charred. Remove to a cutting board, chop into bite-size pieces and add to the bowl with the dressing. Add the raw Tuscan kale, avocado, almonds and tomatoes to the bowl; toss to coat.