Cut 8 ounces tempeh in half crosswise. Cut each half in half lengthwise to create 4 thinner (about 3½-by-1½-inch) tempeh “steaks.” Arrange on a large plate; drizzle with 1½ tablespoons sun-dried tomato oil. Sprinkle with ½ teaspoon pepper and ¼ teaspoon salt. Heat 1 tablespoon sun-dried tomato oil in a large skillet over medium-high heat. Add the tempeh; cook until golden brown and crispy on both sides, 2 to 3 minutes per side. Return to the plate and set aside. Wipe the pan clean.

Heat the remaining ½ tablespoon sun-dried tomato oil in the skillet over medium-high heat. Add shallot; cook, stirring often, until almost softened, 2 to 3 minutes. Add 1½ tablespoons butter; cook, stirring often, until the shallot is soft, about 1 minute. Add chopped sun-dried tomatoes and ¾ cup broth; cook, stirring occasionally, until the liquid has reduced to about ¼ cup. Add 4 cups baby kale; cook, stirring constantly, until wilted, about 1 minute. Reduce heat to medium-low; add ½ cup cream, 1 teaspoon Italian seasoning and the remaining ¼ teaspoon salt. Simmer, stirring occasionally, until the sauce starts to thicken, about 2 minutes. Remove from heat. Add ¼ cup Parmigiano-Reggiano; stir constantly until melted. Nestle the tempeh into the sauce, spooning some over the top. Sprinkle with the remaining ¼ cup Parmigiano-Reggiano and 1 tablespoon basil.