Turn on the oven broiler. Roasted the poblano peppers 15-20 minutes, rotating occasionally, until skin is blistered all over and peppers are tender. Place in a ziploc bag to steam until cool enough to handle. Discard the stems, skins, and seeds. Dice finely.
To a small slow cooker, add the diced poblano pepper, cream cheese, beer, and cheese. Heat on high until creamy smooth (~ an hour; you can turn it to low if you need it to sit a while and you can add more beer to thin it out if it thickens too much). Once the flavors are blended and cheeses are melty smooth, taste and adjust to desired heat level with the hot sauce.
To make the mushrooms, whisk together the flour and seasonings. Slowly whisk in the beer. Let the batter sit a couple minutes for the flour to absorb the beer and for the mixture to thicken.
Heat oil for frying. I used a cast iron skillet with an inch of oil.
Working in batches so as to not overcrowd the oil, dip a few mushrooms in the batter and put in the oil to fry. Turn occasionally to ensure even cooking. Remove to drain on paper towels, Season with a pinch of kosher salt immediately. Repeat with the remaining mushrooms
Serve mushrooms with the queso for dipping.