How to Make It
Place oil and garlic cloves in a small saucepan over low; cook, undisturbed, until garlic is sizzling vigorously, about 7 minutes. Continue to cook, undisturbed, until garlic is tender when pierced with a paring knife, about 5 minutes. Remove from heat; let cool 20 minutes. Remove garlic cloves, and reserve for another use. Set garlic oil aside.
Preheat oven to 350°F. Line bottom and sides of an 8-inch square baking dish with plastic wrap, allowing 3 inches to extend over all sides; set aside. Whisk together ricotta, eggs, Parmigiano-Reggiano, salt, and coriander in a large bowl until thoroughly blended and smooth. Add flour in 2 batches, stirring just until combined after each addition. Stir in 2 tablespoons garlic oil. Spread ricotta mixture in prepared square baking dish; fold plastic wrap sides over ricotta mixture, covering loosely. Cover dish tightly with aluminum foil, and place in a 13- x 9-inch baking dish. Add water to a depth of 1 1/4 inches in the rectangular baking dish.
Bake in preheated oven until slightly firm, 1 hour to 1 hour and 15 minutes. Remove baking dish from water bath; refrigerate, uncovered, until warm, about 1 hour. Cut gnocchi into 1-inch strips; cut or tear strips into irregular 1-inch pieces.
Line a rimmed baking sheet with paper towels. Heat remaining 2/3 cup garlic oil in a 12-inch skillet over medium-high until hot. Reduce heat to medium. Working in 3 batches, place gnocchi in skillet, and cook, turning often with a small offset spatula, until golden brown all over, 6 to 8 minutes per batch. Transfer gnocchi to prepared baking sheet, and season with salt to taste.
To serve, spoon about 1/4 cup roasted eggplant sauce in a circle on each of 4 plates; top evenly with gnocchi. Spoon sautéed eggplant evenly over gnocchi. Pipe small dollops of Parmesan mousse on each serving, and top evenly with pickled peppers. Garnish with basil leaves.