This dish contains no meat, but the filling is chicken broth-based, so it's not vegetarian. You can replace the chicken broth with vegetable broth (buy the boxed version or try this recipe) to make a strictly vegetarian version.
For the pie filling:
• 4 cups canned chicken broth
• 3 large carrots, peeled and cut into ½-inch pieces
• 1 large bunch turnip greens (about 8 to 10 ounces), center stem cut away, leaves cut into 1-inch pieces
• ¼ cup (½ stick) butter
• 4 medium leeks (white and pale green parts only), sliced
• 1 large onion, diced
• 2 cups sliced "baby bella" mushrooms
• 2 tablespoons minced fresh thyme
• ½ cup all-purpose flour
• ½ cup dry white wine
• 1 cup frozen peas
• ½ cup whipping cream
For the crust:
• 2 ½ cups all purpose flour
• 2 tablespoons fresh parsley
• 1 tablespoon fresh thyme
• 1 teaspoon salt
• 1 teaspoon sugar
• ½cup (1 stick) chilled unsalted butter, cut into ½-inch pieces
• ½ cup chilled solid vegetable shortening, cut into ½-inch pieces
• ice water
Butter 4-quart oval baking dish. Pour broth into a large stock pot and to boil; reduce heat to low and add carrots. Simmer uncovered until carrots are just tender, about 10 minutes. Using slotted spoon, transfer carrots to prepared baking dish. Add turnip greens to broth and cook just until wilted, about one minute. Using slotted spoon, transfer greens to colander; drain well. Add to carrots in baking dish.
Strain broth and set aside.
Melt butter in same pot over medium heat. Add leeks, onions, mushrooms, and thyme. Sauté until tender, about eight minutes. Add flour and stir two minutes. Stir in broth and white wine. Increase heat to high and bring to boil, stirring constantly. Add cream and peas and boil until sauce thickens enough to coat spoon, whisking frequently, about six minutes. Season with salt and pepper. Pour gravy over mixture in dish. Stir to blend. Cool 45 minutes. (Filling can be made one day ahead. Cover and refrigerate.)
While the filling is cooling, make the crust. Blend flour, parsley, thyme, salt, and sugar in food processor until herbs are very finely chopped. Add butter and shortening. Blend until mixture resembles coarse meal. Transfer mixture to large bowl. Using fork, mix enough ice water into flour mixture to form moist clumps. Gather dough into ball; flatten into rectangle. Cover and chill 30 minutes.
Position a rack in top third of oven and place baking sheet on bottom rack in oven; preheat to 400 degrees. Roll out crust dough on parchment paper to 15 by 10 by half-inch rectangle. Using paper as aid, turn dough over onto filling. Trim dough overhang; tuck dough edge inside dish. Place pot pie on top rack and bake until crust is golden and gravy is bubbling, about 50 minutes. Let stand 10 minutes before serving.