Preheat oven to 425°F and line a baking sheet with a Silpat or parchment paper.
Wash potatoes and pat dry. Trim a small piece off the top and bottom of the potato. Insert one end of the potato into the spiralizer, lining up the center, and twist to create spirals, letting the spirals fall into a large bowl. When you get near the end of the potato, insert spiralizer top into potato to avoid cutting fingers while finishing the cuts. Repeat with remaining potatoes.
Whisk together olive oil and honey and toss with potatoes.
In a small bowl, mix together paprika, chile powder, salt, and garlic powder. Scatter mixture over potatoes and stir to combine well, making sure the potatoes are evenly coated.
Spread potatoes on prepared baking sheet. If you like, cut spirals into smaller lengths.
Bake for 15 minutes. Sprinkle with oregano and serve immediately.