1 pound squash, cut into 1-inch pieces
1 bunch leeks, chopped
2 garlic cloves, finely chopped
1/4 cup extra-virgin olive oil
1/4 pound carrots, peeled and chopped
1 pound tomatoes, seeded and chopped
1/2 cup corn kernels (from 1 ear)
1 1/2 cups coarsely grated Havarti or Muenster cheese (4 1/2 ounces)
chopped basil or other herbs

1 tablespoon cornmeal (not stone-ground)
4 hard-boiled eggs, peeled and chopped
1 3/4 cups all-purpose flour
1/2 cup cornmeal
1 tablespoon baking powder
3/4 teaspoon salt
3/4 stick cold unsalted butter, cut into 1/2-inch cubes
3/4 cup whole milk plus additional for brushing

Place a heavy baking sheet on middle rack of oven, then preheat oven to 400°F. Toss squash with 1 teaspoon salt, and drain in colander 30 minutes. Cook leeks and garlic in oil, stirring occasionally, until golden, 4 to 6 minutes. Add squash and carrots and cook until vegetables are crisp-tender, 7 to 9 minutes. Remove from heat and stir in tomatoes. Transfer to a large bowl, then toss with corn, cheese, basil, and cornmeal. Season with salt and pepper.
Make crust and bake pie: 
Pulse dry ingredients with butter in a food processor until mixture resembles coarse meal with some roughly pea-size butter lumps. Transfer to a bowl and stir in milk until mixture just forms a dough. Gather dough into a ball and chill, wrapped in plastic wrap, 5 minutes. Halve dough and roll out 1 piece on a well-floured surface with a floured rolling pin into a 13-inch round. Transfer to a 9-inch glass pie plate, leaving overhang. Spread eggs evenly in crust and season with 1/4 teaspoon salt. Add vegetable filling, mounding slightly in middle. Roll out remaining dough in same manner and place over filling. Trim, leaving a 1/2-inch overhang. Press edges of crust together. Fold overhang under and crimp edge all around. Brush crust with additional milk, then cut 3 steam vents. Bake until crust is golden and filling is bubbling, 50 minutes to 1 hour. Cool at least 15 minutes before slicing. Serve warm or at room temperature.