In a large pot over medium-high heat, melt the butter. Add the onion and poblano. Cook, stirring occasionally, until the onion softens, about 7-8 minutes.
Add the garlic, chile powder, and cayenne, and saute for about 1 minute, until fragrant.
Add the chicken broth, and potatoes. Bring to a boil, then lower the heat to maintain a simmer. Cook, stirring occasionally, until the potatoes are tender, about 15 minutes.
Stir in the corn, cream and sweetened. Cook for five minutes, until warmed through.
Transfer 1 ½ cups of the soup to a blender and purée until smooth. Stir the puréed soup back into the pot of remaining soup.
Add stir in the cotija cheese, cilantro, and lime juice and season to taste with salt and pepper, and more sweetener if needed.
Serve garnished with additional cilantro, cotija, Tajín and crema. Serve with lime wedges.