In a large bowl, combine flour and salt. Cut in cold butter using a pastry cutter or fork until mixture resembles coarse crumbs.
Add ice water 1 tablespoon at a time, mixing just until dough holds together.
Divide into two discs, wrap, and chill for at least 30 minutes.
Heat olive oil or butter in a large skillet over medium heat.
Add onion, celery, and carrot; sauté until softened, about 5–6 minutes.
Stir in mushrooms, chickpeas, and pumpkin (or potato) and cook another 8 minutes until tender.
Add garlic, thyme, rosemary, sage, smoked paprika, salt, and pepper; cook 1 more minute.
Sprinkle flour over the mixture and stir well for 1–2 minutes to coat.
Gradually add vegetable broth while whisking, then add milk.
Simmer until thickened, about 5–7 minutes. Stir in peas and corn. Taste and adjust seasoning. Remove from heat to cool slightly.
Preheat oven to 400°F (200°C).
Roll out one chilled dough disc and line the bottom of the deep-dish pie plate, letting edges hang slightly.
Spoon filling evenly into crust.
Roll out the second disc and lay it over the top. Trim and crimp edges to seal. Cut a few small slits for steam.
Brush top crust with milk or egg wash and sprinkle with flaky salt if desired.
Bake 45–55 minutes until crust is golden and bubbling slightly around edges.
Let rest 15–20 minutes before slicing.