Bring 4 quarts of water to a boil in a Dutch oven over high heat. Stir in tablespoon salt and the pasta and cook, stirring occasionally, until just beginning to soften, about 5 minutes. Drain the pasta through a colander and toss with 1 tablespoon of the oil; leave in the colander and set aside.
Wipe the pot dry, then add the remaining 3 tablespoons oil, and set it over medium heat until shimmering. Add the artichokes, onion, and 1 teaspoon salt and cook until the artichokes are lightly browned, 8 to 10 minutes.
Stir in the garlic and lemon zest and cook until fragrant, about 30 seconds. Stir in the flour and cook, stirring constantly, until golden, about 1 minute. Slowly whisk in the broth, wine and cream.
Add the chicken breasts and bay leaves, partially cover, and bring to a simmer. Reduce the heat to low, cover completely, and cook until the thickest part of the chicken registers 160 degrees on an instant-read thermometer, 10 to 15 minutes.
Remove the pot from the heat and discard the bay leaves. Remove the chicken and set aside to cool; keep the sauce covered. When the chicken is cool enough to handle, shred it into bite-sized pieces. Stir the shredded chicken back into the sauce with the cooked pasta, peas, 1 cup of the cheese, and lemon juice; stir until well combined. Season with salt and pepper to taste. Transfer to a 13 by 9-inch baking dish and sprinkle with the remaining cup cheese.
To Store: Wrap the dish tightly with plastic wrap and then foil and refrigerate for up to 2 days or freeze for up to 1 month. (If frozen, the casserole must be thawed completely in the refrigerator, about 24 hours).
To Serve: Thaw completely in refrigerator, about 24 hours. Adjust an oven rack to the middle position and heat the oven to 400 degrees. Unwrap the dish and cover tightly with aluminum foil that has been sprayed with vegetable oil spray (or use nonstick foil). Bake until the sauce is bubbling around the edges, 30 to 40 minutes. Remove the foil and continue to bake until hot throughout and browned on top, 25 to 30 minutes longer. Sprinkle with the tarragon before serving.
To Serve Right Away: Bake the casserole in a 400-degree oven, uncovered, until the sauce is bubbling and the top is browned, 25 to 35 minutes. Sprinkle with the tarragon before serving.