Heat the oil in a 3.5-quart sauté pan (or large skillet) over a medium heat. Add the onion and cook until they just begin to soften (3 to 4 minutes). Add the salt, pepper, and garlic, cook for 1 minute more.
Add the chicken and cook until all sides are lightly browned (5 to 6 minutes) stirring occasionally.
Empty the mixture to a plate and cover with another plate or foil.
Add the butter to the pan and add the chopped mushrooms, thyme and cook for about 3-4 minutes until the mushrooms are beginning to brown. Add the red peppers and cook for 2 to 3 minutes until just beginning to soften.
Sift in the flour and cook for one minute while stirring.
Pour in about ¼ cup of the warm stock and stir to combine. It will form a paste. Continue adding the stock ¼ cup at a time, stirring constantly to avoid a lumpy sauce.
Once all the stock has been added, raise the heat to medium-high and add in the warm milk. Cook, stirring occasionally until the sauce begins to thicken, 3 to 4 minutes.
Add the Dijon and stir to incorporate.
Preheat the broiler with a rack in the middle in the oven.
Add the reserved chicken into the onion mixture (with all the juices) and stir to combine.
Reduce the heat to medium, cover and cook for 5 minutes. Season with salt and pepper at this point, if needed. (Stir occasionally to ensure it is not sticking the bottom of the pan and lower the heat slightly if required.)
Add the peas and cook uncovered until the peas are heated through, and the sauce is the consistency of gravy, about 5 minutes more.