Add some olive oil to a large pot over medium high heat
Add your bell pepper, onion, garlic, jalapeno, and celery – along with some salt and pepper – and let these veggies saute, stirring often, until softened
Add your potato, season with more salt and pepper, and stir to combine
Pour in your chicken stock and bring to a boil. Reduce to a simmer and simmer for 10 minutes
When there are a few minutes left, add your zucchini
Meanwhile, melt your butter in a bowl and whisk in your flour. Set aside
When the time is up, whisk in your butter and flour mixture (roux) to the soup until fully combined (make sure you use a whisk or it could get clumpy). Add your corn at this point, too
Let this simmer for 5 more minutes, until the soup is thickened just a bit and the corn and zucchini are tender
Stir in your half and half, season to taste with salt and pepper, and garnish with fresh basil (optional)