How to Make It
Preheat the oven to 375 F. Spray a 9x13x3-inch (deep) baking pan with vegetable oil.
In a large soup pot or Dutch oven, melt the butter over medium-low heat. Add the onion (if using) and sauté until tender and translucent, 3 to 4 minutes. Add the carrots and cook until slightly softened, about 4 minutes. Stir in the flour and cook for 1 minute, stirring often and scraping the bottom of the pot.
Whisk in the chicken broth and continue whisking until the flour is fully incorporated. Stir in the chicken soup. Increase the heat to medium-high and bring to a gentle boil. Simmer for 5 minutes.
Remove from the heat and stir in the shredded chicken and frozen peas. Taste and season if necessary with salt and pepper. Pour the mixture into the prepared baking dish.
Open one can of crescent dough an unroll the contents onto a surface. Press the perforations together inside each rectangle to make a single rectangle. Set it on top of the stew in the pan, flush against one long side; it will cover about two thirds of the surface. Open the second can of crescent dough and unroll the contents onto a surface. Set aside half of the dough. Press the perforations together inside the two remaining rectangles to make one long rectangle. Place it on the uncovered part of the stew, easing it into the space without overlapping it with the dough that is already there. Tuck the corners and edges in if necessary. The dough should fit pretty neatly on top without needing to crimp the edges. (If desired, form small crescent rolls with the remaining dough and bake them separately.)
Bake until the crust is nicely browned and the stew is bubbling around the edges, 15 to 20 minutes. Let stand for 5 minutes.
For each serving, place mashed potatoes in the center of a shallow pasta plate and spoon over a generous amount of stew and crust, so that the potatoes are completely covered. Serve.
Store leftovers in a covered container in the refrigerator for up to 2 days.