Vegetable and Goat Cheese “Lasagna”

Name: Vegetable and Goat Cheese “Lasagna”
Ingredients: Two ¼-pound baby eggplants (about 4½ inches long), ends trimmed, skin partially removed, and cut lengthwise into 1/8-inch slices; Kosher or sea salt; 2 tablespoons pine nuts; 1 bunch (about 4 ounces) arugula, stems trimmed; 1 bunch (about 6 ounces) watercress, stems trimmed; 6 tablespoons extra virgin olive oil; 1 tablespoon white wine vinegar; ¼ teaspoon sugar; Freshly ground pepper; Two ¼-pound zucchinis, ends trimmed (about 4½ inches long), cut lengthwise into 1/8-inch slices; About 3 ounces fresh goat cheese, cut from a 1½-inch-wide log, in 1/8-inch crosswise slices; ¼ teaspoon sweet paprika, preferably Spanish smoked; ¼ pound cherry tomatoes, in ½-inch slices, ends discarded; 2 teaspoons nonpareil capers; 2 cloves garlic, minced; About 3 ounces mushrooms, preferably oyster mushrooms, separated into ears, or other mushrooms like shiitake, in ¼-inch lengthwise slices; 4 piquillo peppers, or 2 pimientos, preferably home prepared, cut in long 1/8-inch-wide strips; 1 tablespoon fresh basil leaves, coarsely chopped, or ½ teaspoon dried; Extra virgin olive oil for drizzling; 2 tablespoons grated well-cured Manchego or Parmesan cheese; 2 tablespoons minced parsley