Heat a small frying pan over medium high heat and add a little olive oil. Add in the chicken, then add the veggies around the chicken. Season with salt and pepper. Cook about 3 minutes to brown the chicken, stirring the veggies as the chicken cooks.
Flip the chicken and cook another 3 minutes to brown the other side. Add in the garlic and cook 2 minutes, stirring the garlic into the veggies.
Add in the chicken stock and stir to combine. Bring to a simmer, reduce the heat to low, and cover. Cook until the chicken is cooked through, about 15 minutes.
Remove the chicken from the pan and chop/shred it up.
Add the milk to the pan, along with the parsley, potato flakes, and frozen peas. Stir to combine. Add in the chicken and bring to a simmer. Cook about 2 minutes, it should be fairly thick, but if not, you can add a little more of the potato flakes. Allow to cool.
Roll out the dough in a pasta maker, folding it over itself and repeating until smooth. Roll it out to the third thinnest setting.
Cut out about 3 inch rounds of the dough. Use a small bowl and add one of the rounds to the bowl. Fill with the filling and top with another dough round.
Seal the dough with a fork to make it look like a pie. Remove from the bowl and flatten it a bit so it looks like a pie. Re-do the fork outline if needed.
Repeat with the remaining filling and dough until you make enough to have 2 per person.
Boil the ravioli in batches until the pasta is tender, about 3-5 minutes.
Serve over mashed potatoes and top with the gravy.