For the mashed potatoes: In a medium pot, cover the potatoes with cold water and bring to a boil until fork-tender, 35 to 40 minutes.
Drain and transfer the potatoes to a stand mixer fitted with the paddle attachment. Add the butter and milk, and season with salt. Beat until incorporated and smooth. (You can also hand mash the potatoes.)
Carefully transfer the mixture to a piping bag fitted with a star tip.
For the filling: Heat oven to 375 F.
In a large skillet, bring the olive oil to medium heat. Add the ground beef, breaking it up with a wooden spoon or spatula. Season with salt and pepper and brown the beef completely. Remove the browned ground beef from the pan and set aside. Discard any excess fat from the pan.
Return the pan to medium heat and add the carrots, onions, celery and garlic and sauté until tender and fragrant, about 7 minutes.
Add the mushrooms and sauté for 2 minutes more.
Remove the pan from the heat, pour in the red wine and stir.
Return the pan to the heat and stir in the tomato paste, flour, Worcestershire sauce, Dijon mustard and beef stock, and bring to a simmer, stirring periodically, until the sauce thickens and coats the back of a spoon 3 to 5 minutes.
Stir in the browned ground beef, bay leaf, thyme leaves, peas and corn, and cook for 2 minutes, then remove from heat.
Divide the filling mixture evenly between 4 16-ounce crocks and pipe the mashed potato mixture on top of the filling in quarter-size dollops.
Bake for 35 minutes. The top of the pie will be lightly golden and beginning to crisp. You can broil on high for 1 to 2 minutes if your potatoes haven’t begun to brown after 35 minutes.
Let the pies rest for 5 minutes and serve hot.