Line a large rimmed baking sheet with paper towels. Arrange sliced zucchini, flat-side down, on the prepared baking sheet. Sprinkle with ¼ teaspoon salt; let stand until water leaches out, about 10 minutes. Pat dry with paper towels.

Heat 1 tablespoon sun-dried tomato oil in a large skillet over medium heat. Add 4 cups of the zucchini, flat-side down; cook, undisturbed, until browned, about 4 minutes. Flip and cook, undisturbed, until browned on the other side, about 2 minutes. Stir and continue to cook, stirring occasionally, until tender, 2 to 4 more minutes. Transfer to a large plate. Repeat the process with 1 tablespoon sun-dried tomato oil and the remaining 4 cups zucchini. Do not wipe the skillet clean.

Heat the remaining 1 tablespoon sun-dried tomato oil in the skillet. Add ⅔ cup sun-dried tomatoes, the chopped shallot and the remaining ¼ teaspoon salt; cook, stirring constantly, until slightly softened, 2 to 3 minutes. Add the chopped garlic, 1 teaspoon Italian seasoning, ½ teaspoon crushed red pepper and ½ teaspoon smoked paprika; cook, stirring constantly, until fragrant, about 1 minute.

Stir 1¼ cups broth into the tomato mixture. Bring to a lively simmer and cook, stirring occasionally, until slightly reduced, about 3 minutes. Stir in ¼ cup cream. Return to a lively simmer; stir in 2 ounces cream cheese until melted and combined, about 2 minutes. Remove from heat; stir in ½ cup basil and the cooked zucchini. Sprinkle with 2 tablespoons Parmesan. Garnish with additional crushed red pepper and basil, if desired.