Bring a pot of salted water to a boil. Gently poach the fingerlings for 5 minutes. Drain the potatoes, cut in half and dry thoroughly.
Heat a large pan over medium-high heat. Melt the butter, add the leeks and season with salt and pepper. Saute until softened, about 8 minutes. Set aside.
In the same pan, heat the olive oil. Put the fingerlings cut-side down in the pan and cook until golden brown, about 5 minutes; flip and repeat on the skin side. Add back the leeks, drizzle with the honey and cook for another 2 to 3 minutes.
Sprinkle with the parsley and lemon zest. Season with additional salt and pepper to taste.