Cut bread into 1-in. cubes and spread them on a baking sheet or clean counter. Let sit overnight.
Preheat oven to 350°. With a fork or sharp knife, poke holes all over squash. Microwave it on high 10 minutes. Let sit until cool enough to handle. Halve squash lengthwise; scoop out and discard seeds. Flesh should be tender when scraped with a fork; if it isn't, microwave on high (cut side down) in 1-minute intervals until tender.
Scrape flesh from 1 squash half into a blender. Whirl with 2 cups half-and-half, the granulated sugar, nutmeg, and five-spice powder until smooth. Add eggs and whirl just to combine.
Put bread cubes in a large bowl and pour half the egg mixture over them. Stir remaining 1 cup half-and-half into remaining egg mixture and pour entire mixture over bread. Let sit 30 minutes.
Meanwhile, scrape flesh from other squash half into a medium bowl. Add brown sugar and mash coarsely with a fork.
Gently stir mashed squash into bread mixture. Butter a 9- by 13-in. pan and pour mixture into pan. Bake until set in the center, about 30 minutes. Serve warm, with Tres Leches Sauce.
Note: Nutritional analysis is per serving without sauce.