Preheat oven to 400°. Spray 30 wells of 2 (20-well) mini muffin pans* with cooking spray.
Using a mandoline, cut 30 thin slices from short end of potato. Arrange slices over wells of prepared muffin pans.
Bake until potato slices are pliable, approximately 15 minutes. Press potato slices into wells so they conform to well shapes. Bake until crisp, approximately 15 minutes more. Let cool completely in muffin pans before removing.
In a large sauté pan, heat oil over medium heat. Add garlic; cook until fragrant, approximately 3 minutes. Add spinach, artichoke hearts, salt, pepper, and sage; cook until spinach wilts, 6 to 8 minutes.
Divide spinach mixture among potato cups. Serve immediately.