Add the olive oil to a large saucepan over medium-high heat. Once the oil is hot, add half of the beef and cook for 1-2 minutes, browning all over. (Note: the meat doesn’t need to be completely cooked). Transfer to a plate and repeat with the remaining beef. Set aside.

Turn the heat down to medium and add the butter, scraping up any brown bits from the bottom of the pan as it melts. Add the onions, carrots, celery, 1/2 teaspoon salt, and 1/2 teaspoon pepper, then cook until vegetables begin to soften, 4-5 minutes. Add the flour and cook for 1 minute, stirring constantly. Add the tomato paste, stir for 1 minute, then add the broth, milk, potatoes, and thyme.

Bring the mixture to boil over medium-high heat, then reduce the heat to medium-low and simmer until the sauce is thickened and the potatoes are tender, 8-10 minutes. Remove from the heat and stir in the beef (as well as any juices that have accumulated on the plate) and peas.

On a clean, floured surface, roll out one of the discs of chilled dough into a 12-inch diameter circle (keep the second disc refrigerated). Place the dough into a 9-inch pie dish that’s 1 1/2 to 2 inches deep. Smooth out the dough inside the dish, then trim and discard the overhang of dough.

Pour the beef mixture into the dish.

Roll out the second disc of dough and use it to cover the pie, again trimming the extra overhang. Crimp the dough around the edges using a fork, then use a knife to cut a few small slits in the top center of the dough to allow steam to escape while cooking.