1. Bring a medium pot of water to a boil, and generously season with salt. Add celery root, and simmer 3 minutes. Add potatoes and sweet potatoes, and simmer vegetables 2 minutes more. Drain well, and spread vegetables on a rimmed baking sheet. Let cool 15 minutes.

2. Heat 2 tablespoons oil in a large (preferably cast-iron) skillet over medium-high heat, and cook onions until translucent and just beginning to color, about 2 minutes. Add remaining 2 tablespoons oil, the apples, and vegetables; season with salt and pepper. Stir to combine, then press into a single layer using a spatula. Cook, undisturbed, 2 minutes. Stir, and repeat process until vegetables are very tender and beginning to caramelize, 8 to 10 minutes more. Remove from heat. Stir in sage, and season with salt and pepper.