Combine eggplant and 2 tablespoons salt in a large bowl with water to cover. Place a plate on top of the eggplant to weigh it down and keep it covered in water for about 30 minutes. Drain and rinse eggplant in cool water. Pat dry and cut into cubes.
Combine tomato puree, 1 teaspoon rock salt, garlic, and basil in a saucepan over medium-low heat. Simmer, stirring occasionally, until sauce flavors combine, 5 to 10 minutes.
Meanwhile, heat olive oil in a skillet over medium-high heat. Saute eggplant until golden brown, 5 to 10 minutes. Drain on paper towels.
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain and toss with the tomato-basil sauce; divide into 4 serving bowls. Top with eggplant. Sprinkle 1/4 the ricotta and 1/4 the diced pepper over each bowl.