Cover potatoes with 2 inches of water in a saucepan; add 1 tablespoon salt. Bring to a boil, then reduce heat to medium and simmer until potatoes are tender when pierced with the tip of a knife, 4 to 5 minutes. Using a slotted spoon, transfer to a plate. Add broccoli to pan; return to a boil and cook 1 minute. Drain and coarsely chop.

Heat a large skillet over medium-high; swirl in oil. Add cumin and mustard seeds and coriander; cook, stirring, until fragrant and mustard seeds begin to pop, 30 to 60 seconds.

Add onion, ginger, serrano pepper, garlic, and 1 teaspoon salt. Cook, stirring frequently, until onion is translucent, about 3 minutes. Add potatoes and cook, stirring and mashing with the back of a fork, until mixture has the texture of very chunky mashed potatoes. Stir in broccoli and cilantro; season with salt. Let cool completely, about 30 minutes.

Preheat oven to 400°. On a lightly floured surface, roll dough out to a 14-by-10-inch rectangle; trim edges. Cut in half crosswise to create two approximately 7-by-10-inch rectangles. Transfer one rectangle to a parchment-lined baking sheet; arrange filling down the center, leaving a 1-inch border. Brush border with egg. Top with second rectangle of dough; press edges to seal. Cut six 2-inch vents in top. Freeze 15 minutes.

Brush top of pie with egg and bake until puffed and golden brown, 40 to 50 minutes (if browning too quickly, tent with foil). Let cool at least 30 minutes, then cut into squares and serve.