How to Make It
Preheat oven to 400°.
Place bread cubes onto a rimmed baking sheet. Bake at 400° for 15-20 minutes or until golden brown, stirring once. Remove from oven and let cool at least 5 minutes.
Heat butter and 1 1/2 teaspoons oil in a medium skillet over medium-high heat. Add onion mixture and sage to pan; cook 4-5 minutes or until tender, stirring occasionally. Remove from heat. Combine stock and eggs in a medium bowl, stirring with a whisk. Add bread, onion mixture, parsley, 1/2 teaspoon salt, and pepper; toss to coat and let stand 10 minutes or until liquid is absorbed, stirring after 5 minutes.
Cut top ¼ off carnival squash. With a spoon, scrape out and discard seeds and pith; leaving a ¾-inch edge inside squash. Cut thin slice from bottom of squash so they sit flat and level. Divide bread mixture evenly among squash. Arrange on a baking sheet lined with parchment paper. Bake at 400° for 35 minutes or until tender when pierced with a sharp knife.
While squash bakes, cut entire neck of butternut squash from bulb, reserving bulb for another use. Cut neck in half lengthwise; reserve one half for another use. Place remaining neck half, cut side down, on cutting board. Cut lengthwise into 1/8-inch-thick slabs. Using a vegetable peeler, cut ribbons from flesh side of each slab.
Combine remaining 11 /2 teaspoons oil and honey in a small bowl. Arrange 12 squash ribbons in a lattice design (6 horizontal ribbons and 6 vertical ribbons) on a cutting board or work surface. Repeat 3 more times to build 4 lattice tops. After squash has baked until tender, carefully transfer each lattice to top each squash (use a fish spatula or thin metal spatula to lift lattice). Using scissors, trim edges of lattice so the overhang measures about 1 inch. Brush lattices with honey mixture. Sprinkle lattices evenly with remaining 1/4 teaspoon salt. Bake at 400° for 10 minutes.