In a large dutch oven, heat the butter over medium high heat.
Add the onions, carrots, and celery and cook for 4-5 minutes or until the vegetables soften.
Add the garlic, jalapenos, and potatoes and cook for 3-4 minutes, stirring so the veggies don’t stick to the pot.
Add the broth, bay leaf, and thyme, bring to a boil. Cover, lower the heat and let simmer for 8-10 minutes or until the potatoes are half way cooked.
Add the zucchini and corn kernels and continue to cook for an additional 5-7 minutes or until the potatoes are cooked through. You can check the doneness by gently piercing with the tip of a knife.
Remove the bay leaf, transfer 2 cups or more (see notes) into a food processor and process until smooth.
Pour the blended mixture back into the pot.
Heat the soup over medium high heat, add the half and half and let come to a gentle simmer.
Serve topped with fresh parsley and smoked paprika if desired.