How to Make It
Arrange the eggplant slices on a work surface and sprinkle with salt. Transfer the eggplant to a colander, top with a plate and weight it down with heavy cans. Set the colander in the sink and let the eggplant drain for 1 hour.
Meanwhile, preheat the oven to 425°. Brush the squash slices on both sides with olive oil and arrange them on 2 large baking sheets. Season with salt and pepper and bake for about 25 minutes, or until tender and golden brown.
Pat the eggplant slices dry. Brush them on both sides with olive oil and arrange on 2 large baking sheets. Bake for 25 minutes, or until tender and golden brown. Transfer the eggplant to a plate. Turn the oven down to 350°.
In a medium skillet, heat 1 tablespoon of the olive oil. Add the chicken and scallions and cook over moderately low heat, stirring, until the chicken is white throughout, about 5 minutes. Transfer to a food processor. Add the capers and the remaining 1 tablespoon of olive oil and season with salt and pepper; process to a coarse paste.
Roast the bell pepper directly over a gas flame or under the broiler until charred all over. Transfer the pepper to a bowl, cover with plastic wrap and let steam for 5 minutes. Peel the pepper and discard the core, seeds and stem. Cut lengthwise into 1/4-inch-thick strips.
Lightly grease a large baking dish. Line the dish with half of the eggplant slices. Spread half of the pureed chicken over the eggplant and sprinkle with half of the Gruyère. Top with the squash slices and drizzle with 3 tablespoons of the beaten eggs. Top with the remaining chicken, Gruyère and eggplant slices. Arrange the bell pepper strips over the eggplant in a lattice pattern. Pour the remaining beaten eggs evenly over the filling, tilting the dish as necessary.
Cover the tagine with foil and bake for 20 minutes. Uncover and bake for about 20 minutes longer, or until the tagine is bubbling hot and the eggs are set. Let stand for at least 20 minutes and for up to 2 hours before serving.