Preheat an outdoor grill for high heat, 400 degrees F or 200 degrees C, and lightly oil the grate.

Lightly spray or brush poblano peppers with olive oil. Cook peppers on the preheated grill, turning every couple minutes, until charred and softened, 5 to 8 minutes.

Remove peppers from the grill and place in a large resealable plastic bag to steam, about 15 minutes. Peel off charred skins. Discard seeds and chop peppers.

Melt butter in a saucepan over medium-high heat. Add flour and cook, stirring, about 1 minute. Add onion and cook for 1 minute more. Whisk in milk slowly and cook, stirring constantly, until slightly thickened, 3 to 5 minutes. Reduce heat to low and add Monterey Jack cheese, cream cheese, salt, paprika, pepper, red pepper flakes, and cayenne; whisk until cheeses have melted and are blended in, about 5 minutes. Stir in chopped poblano peppers.