Step 1

Heat 1 Tbsp. extra-virgin olive oil in a large skillet over medium. Add 2 Tbsp. unsalted butter and swirl to melt. Add 2 shallots, thinly sliced, stir to coat, and season with ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt. Cook, stirring occasionally, until shallots are beginning to brown around the edges, about 5 minutes. Add 1 bunch Tuscan kale, ribs and stems removed, leaves sliced, and cook, stirring occasionally, until wilted, about 3 minutes. Remove pan from heat.

Step 2

Whisk 5 large eggs, 4 sprigs thyme, leaves picked, finely chopped, 2 sprigs rosemary, leaves picked, finely chopped, one 15-oz. can pumpkin purée, 2 cups whole milk, 1 cup heavy cream, 1 Tbsp. Dijon mustard, ¼ tsp. freshly grated ground nutmeg, and remaining 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt in a large bowl until smooth; season generously with freshly ground black pepper.

Step 3

Butter a 3-qt. baking dish with unsalted butter. Scatter ½ large loaf ciabatta or country-style bread, torn into 3"–4" pieces, across bottom of dish, then top with half of kale mixture. Sprinkle a third of 10 oz. aged cheddar, coarsely grated, over; pour in half of egg mixture. Repeat layers with remaining bread and kale mixture, then half of remaining cheese and remaining egg mixture. Top with remaining cheese. Cover pan with foil; chill at least 1 hour and up to 1 day.

Step 4

Preheat oven to 350˚. Let strata sit at room temperature 15 minutes.

Step 5

Bake strata 45 minutes. Remove foil, increase heat to 400˚, and continue to bake until custard is bubbling around the edges and top is puffed, golden, and crisp, 20–30 minutes more. Let cool 10 minutes before serving (strata will deflate slightly as it cools).