This rustic-yet-elegant tart combines buttery leeks and scallions with creamy, bright goat cheese, and cradles them together inside a crisp and tender rye-flour crust.
Preheat oven to 375°F. On a lightly floured surface, roll dough into an 11-by-14-inch rectangle, about 1/8 inch thick. Fit into an 8-by-11-inch fluted tart pan with a removable bottom; trim edges. Dock bottom with a fork and refrigerate 20 minutes.
Line chilled dough with parchment and fill with dried beans or pie weights; bake until dry to the touch, 35 to 40 minutes. Carefully remove beans and parchment and bake until golden brown all over, 10 to 15 minutes more. Transfer to a wire rack and let cool at least 30 minutes. (Baked crust can wrapped in plastic and stored at room temperature up to 1 day.)
Melt butter in a large skillet over medium heat. Add leeks, season with salt and pepper, and cook, stirring gently, until just turning light golden, about 2 minutes. Add 1/4 cup water; cover and cook until just tender, 3 to 5 minutes. Add scallions and cilantro; remove from heat. Season with salt and pepper and let cool 15 minutes.
Meanwhile, in a food processor, combine cheese, eggs, milk, cream, 1/2 teaspoon salt, and 1/4 teaspoon pepper; pulse to combine. Pour into crust. Top with leek mixture, spreading evenly. Bake until set in center, 22 to 25 minutes. Transfer to wire rack and let cool in pan at least 15 minutes. Serve warm or at room temperature. (This tart is best eaten the day it is made, but can also be refrigerated, wrapped in plastic, up to 2 days.)