In a large pot, combine the chicken stock, corn cobs, 3/4 lb of potatoes (cut into 1/2-inch cubes), and bay leaf. Bring to a boil over medium-high heat, then reduce to low and simmer for 20 minutes until the potatoes are completely soft and falling apart. This infuses the stock with corn flavor while cooking the potatoes for blending. Remove the corn cobs and bay leaf with a slotted spoon or tongs, then carefully blend the potato mixture until completely smooth using an immersion blender or regular blender. Set the blended stock aside.
Heat the butter and olive oil in the same large pot over medium heat until the butter is foaming. Add the diced onion and cook for 5-7 minutes, stirring occasionally, until softened and translucent. The butter and oil combination creates a richer base and helps develop the onion's sweetness. Stir in the minced garlic and cook for 30 seconds until fragrant.
Add the diced carrot, celery, bell pepper, corn kernels, and remaining 1/2 lb of potatoes (cut into 1/2-inch cubes) to the pot. Stir to combine with the aromatics, then cover and cook on low heat for 15 minutes, stirring occasionally, until all vegetables are tender. I like to keep the vegetables in smaller cubes than traditional chowders—it gives you more vegetable in every spoonful and makes the texture more interesting.
Pour the blended corn stock from Step 1 into the pot with the cooked vegetables. Bring to a gentle boil over medium-high heat, then reduce to low and simmer for 2 minutes to allow the flavors to meld. Season with salt, smoked paprika, and freshly ground black pepper to taste. I find the smoked paprika adds a subtle depth that makes people ask what the secret ingredient is—it's more interesting than plain paprika here.
Ladle the chowder into bowls and garnish each serving with fresh chopped basil. The bright basil adds a fresh contrast to the creamy, earthy chowder.