Cut the stems and tops off each artichoke. Remove the tough outer leaves. Snip the ends off the remaining leaves with scissors to remove thorns. Remove the tough exterior of the stems and cut them in half. Set aside.

Combine bread crumbs, pecorino Romano cheese, mint, garlic, salt, and pepper in a bowl. Drizzle with olive oil and mix well.

Wiggle an artichoke back and forth with your thumbs to open the leaves. Stuff the bread crumb mixture between multiple leaves and in the center. Repeat with the second artichoke.

Place artichokes and stem pieces in a large pan that has a tight-fitting lid. Add wine and water to the pan, making sure not to wet the artichokes. Cover and bring to a boil. Reduce to a simmer and cook until you can easily pull an outer leaf off an artichoke, about 1 hour.