Preheat oven to 350 degrees F.
Cut each squash in half from stem to base by inserting sharp chef's knife and carefully rocking back and forth. Scoop out seeds and discard. Place squash halves face down on parchment lined baking sheet.
Bake in preheated oven for 30 minutes. The goal is not to fully cook the squash but to soften it enough to make peeling and cutting easier.
Once squash is cool enough to handle, use a vegetable peeler or sharp knife to remove skin. Cut flesh into 1-inch sized cubes. Transfer cut squash to a very large bowl.
Increase oven temperature to 425 degrees F.
In a small bowl, whisk together flour, corn starch, pumpkin pie spice, salt, and pepper. Add mixture to squash and toss to coat. Once all the pieces are lightly coated, discard any additional flour mixture, if any.
In a small sauce pan, melt butter with sage over medium high heat, whisking constantly. Continue to cook while continually whisking until butter gets hot and foamy, sage gets crispy, and brown solids start to form. Once you have brown butter, remove from heat and stir in maple syrup.
Pour butter mixture over flour coated squash, toss to coat, and then transfer to a parchment lined baking dish. Spread into a single layer.
Bake in 425 degree F oven for 30-45 minutes, turning at least once, until golden brown. Once squash is soft, you can increase heat to broil in order to get more of a top crust. Add additional salt, if desired. Transfer to a serving dish and serve hot.