Add poblano and jalapeno peppers to a foil-lined baking sheet and broil on low, flipping halfway through, until charred. Peel off charred skin when cool enough to handle.
Melt butter in a medium-sized pot over medium heat. Add onion and garlic and sauté for a few minutes. Add flour and salt and cook for a few more minutes, as you stir. Add broth and whisk to combine.
Remove seeds from the peppers, then dice. Add to the pot, along with the diced potato. If you'd like some texture in your soup, leave one of the chopped poblanos to add after you puree the other peppers in the soup.
Add jalapeno juice and bring to a boil. Turn heat to low, cover, and simmer on low heat for 30 minutes.
Use a hand-held immersion blender to blend the soup until creamy. Stir the reserved chopped poblano and half-n-half into the soup before serving.
Notes
If you want an even creamier texture and don't mind the extra fat, add heavy cream to your crema de poblano soup.
If you like a chunkier soup, feel free to add some canned/drained black beans and corn kernels.
If you prefer milder soup, you can leave out the jalapeno pepper.
To increase the amount of protein, make chicken poblano soup by adding shredded rotisserie chicken.
Leftovers can be stored in an airtight container for up to 5 days in the fridge.
I don't recommend freezing poblano soup, especially after adding half and half.