Step 1

Combine flour, cheese, thyme and salt; cut in butter until crumbly. Gradually add ice water, tossing with a fork until dough holds together when pressed. Shape into a disk; refrigerate 1 hour.

Step 2

For filling, melt butter in a large saucepan over medium-high heat. Add carrots, celery and onion; cook and stir until slightly softened, 5-7 minutes. Add mushrooms; cook 3 minutes longer. Add Swiss chard and garlic; cook until chard is wilted, 2-3 minutes.

Step 3

Whisk together broth, flour, salt and pepper; slowly pour over vegetables, stirring constantly. Cook until thickened, 2-3 minutes. Stir in chicken and oregano.

Step 4

Preheat oven to 400°. On a floured parchment sheet, roll dough into a 12-in. circle. Transfer to a baking sheet. Spoon filling over crust to within 2 in. of edge. Fold crust edge over filling, pleating as you go, leaving center uncovered. Bake on a lower oven rack until crust is golden brown and filling is bubbly, 30-35 minutes. Cool for 15 minutes before slicing. Sprinkle with parsley.