Fall Squash and Leek Bread Pudding

Name: Fall Squash and Leek Bread Pudding
Ingredients: 4 tablespoons unsalted butter, plus more for pan; 12 cups (1 pieces) brioche (from about 2 loaves); 1 small butternut squash (about 1 1/2 lb.), peeled, seeds removed, cut into 1/2 pieces; 2 large leeks, white and pale green parts only, halved lengthwise, cut into 1/2 pieces; 1 teaspoon thyme leaves; 2 teaspoons kosher salt, plus more; 4 large eggs; 3 cups heavy cream; 3 cups whole milk; 1 teaspoon sugar; 1 1/2 cups coarsely grated Emmenthal cheese, Comté, and/or aged Gouda, divided; Crème fraîche and fennel fronds (for serving)