Prep the pan and oven: Heat the oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or oil.
Toast the bread: Spread the bread cubes on a sheet pan and bake for 8–10 minutes until dry and lightly golden.
This helps the custard soak in without turning soggy.
Cook the vegetables: Heat the oil or butter in a large skillet over medium. Add the onion and a pinch of salt; cook 5–7 minutes until translucent. Stir in the squash and cook 5–8 minutes until just tender and lightly golden.
Add garlic in the last minute. Season with salt, pepper, and red pepper flakes if using. Set aside to cool slightly.
Make the custard: In a large bowl, whisk the eggs, milk, cream, honey, Dijon, 1 teaspoon salt, and pepper until smooth.
Taste a drop—if you want a touch more sweetness, add a bit more honey.
Assemble: In the greased dish, combine the toasted bread, cooked vegetables, most of the cheese, and the herbs. Toss gently to distribute everything evenly.
Add the custard: Pour the egg mixture over the bread and squash. Press down lightly with a spatula to help the bread soak it up.
Let it sit for 10–15 minutes (or up to 30) so the liquid absorbs well.
Top and bake: Scatter the remaining cheese on top. Bake for 35–45 minutes, until puffed, golden, and set in the center. A knife inserted should come out mostly clean with a few moist crumbs.
Finish and rest: Let the pudding rest 10 minutes.
Drizzle with a thin ribbon of honey and sprinkle more herbs or a little lemon zest if you like.
Serve: Cut into squares or spoon it out. It’s lovely warm, with a simple green salad or sliced tomatoes on the side.