Over medium-high heat, cook collards in water and chicken broth for 20 minutes. Drain and set aside. Pour oil into pan. Over low heat, stir in coconut oil and heat until melted. Stir in onion, coating well. Increase heat to medium and stir occasionally, for 5 minutes or until much of moisture is gone and onion is limp and steamed well. Stir in apples, honey, and white pepper, thoroughly combining. Continue to cook, stirring frequently for 5 additional minutes or until apples are limp and volume is reduced. Increase heat to medium-high; cook for an additional 10 minutes, stirring frequently. Continue to cook for another 10 minutes, stirring more frequently. At this time, the caramelizing will be noticed. Do not leave the onions and apples as the mixture will need constant stirring due to burning easily. Cook for another 10 minutes, stirring constantly. Push onion-apple mixture to one side; pour in wine and stir to loosen all brown bits, deglazing pan. Stir apple, onions, and browned bits together. Remove from heat and stir in collards.
Serve immediately.