Line a large rimmed baking sheet with heavy-duty foil and spray it lightly with a cooking spray. Add the potatoes, drizzle with 2 tablespoons of the olive oil then toss to coat. Sprinkle with ¼ teaspoon of the kosher salt and ¼ teaspoon freshly cracked black pepper.
Roast the potatoes in a 400-degree oven for about 40 minutes, or until tender. Stir the potatoes after about 20 minutes.
While the potatoes are roasting, melt the butter with the remaining 2 tablespoons of olive oil in a large stockpot over medium heat. Add the leeks and onion, and season with the remaining ¼ teaspoon of black pepper.
Cook the leeks and onion until they are soft and translucent, about 10 to 12 minutes. Add the remaining ½ teaspoon of kosher salt, along with the roasted potatoes, chicken stock, white wine and the concentrated chicken base.
Using an immersion blender, puree the ingredients until smooth.
Pour in the half and half and continue cooking until warmed through. Check for seasoning, adding more kosher salt and black pepper to suit your taste.
Serve with a sprinkling of shredded white cheddar cheese.