Adjust an oven rack to the middle position and heat the oven to 300°F.
Pulse the bread and butter in a food processor to coarse crumbs, about 6 pulses. Spread the crumbs out over a rimmed baking sheet. Bake, stirring occasionally, until golden and dry, 20 to 30 minutes.
Let the crumbs cool, then toss with the parsley; season with salt and pepper to taste.
MAKE THE CASSEROLE:
Melt butter in a Dutch oven over medium heat. Add the onion and 1 teaspoon salt and cook until softened and lightly browned, 5 to 7 minutes. Stir in garlic and cayenne and cook until fragrant, about 30 seconds. Stir in flour and cook, stirring constantly, until golden, about 1 minute. Slowly whisk in the broth and cream.
Add chicken breasts, partially cover and bring to a simmer. Reduce the heat to low, cover completely, and cook until the thickest part of the chicken breast registers 160°F. on an instant-read thermometer, 10 to 15 minutes.
Remove the chicken with a slotted spoon and set aside to cool. Stir the rice into the pot, cover and continue to cook over low heat, stirring often, until the rice has absorbed much of the liquid and is just tender, 20 to 25 minutes.
Meanwhile, when the chicken is cool enough to handle, shred it into bite sized pieces.
Remove the pot from the heat and stir in the shredded chicken, peas and carrots, cheddar, and lemon juice. Season with salt and pepper to taste. Pour the mixture into a 13x9 inch baking dish and sprinkle with the crumb topping.
Adjust oven rack to middle position and heat the oven to 400°F. Cover tightly with aluminum foil. Bake until the casserole is bubbling and hot throughout, about 1 hour. Remove foil and continue to bake until the crumbs are crisp, 15 to 20 minutes longer. Sprinkle with parsley before serving.