Whisk together the garlic and juice of 1 1/2 of the lemons in a small bowl. Let stand for 5 minutes to mellow the garlic flavor. Whisk in the olive oil and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Set aside.
Bring a large pot of salted water to a boil and prepare an ice bath. Squeeze the juice from the remaining lemon half into the boiling water and add the rind to the water. Add the artichokes and cook until the centers are tender when pierced with a knife, about 8 minutes. Shock the artichokes in the ice bath, remove from the water and pat dry.
Heat a grill pan over medium-high heat.
In a large bowl, toss the artichokes with about 1/4 cup of the dressing. Place the artichokes on the grill pan and cook until grill-marked, 3 to 4 minutes per side. Set aside.
Preheat the oven to 200 degrees F.
Set up 3 shallow bowls or baking dishes. In one, mix together the flour, 1/2 teaspoon salt and 1/4 teaspoon pepper. In the next one, whisk together the eggs, 1/4 cup water and some salt and pepper. In the last one, mix together the breadcrumbs, Parmesan and salt and pepper to taste. Coat each chicken piece with the flour mixture first, shaking off any excess flour. Next, dip into the egg mixture, making sure to coat both sides. Lastly, dredge in the breadcrumb mixture, pressing lightly to coat. Place on a baking sheet fitted with a rack.
In a large skillet, heat the canola oil over medium heat. Add 3 or 4 chicken pieces and cook each side until golden brown, 3 to 4 minutes. Transfer to a clean baking sheet fitted with a rack and hold in the oven. Repeat the process with the remaining chicken.
To serve, toss the watercress with the remaining dressing. Place each chicken piece on a plate, arrange some of the artichokes around the chicken, top with some of the watercress and serve.