Rinse and drain mushrooms and trim off tough stem ends. Gently snap off stems; finely chop stems.
In a 10- to 12-inch frying pan over high heat, frequently stir half the mushroom caps in 1 tablespoon butter until browned on both sides, about 7 minutes. Pour into a bowl and repeat to brown remaining mushrooms in 1 more tablespoon butter; pour into same bowl.
To unwashed pan, add another tablespoon butter, chopped mushroom stems, and shallots; stir often over high heat until lightly browned, about 6 minutes. Divide mixture equally between two small bowls.
Rinse chili. Wearing rubber gloves, cut chili in half lengthwise and remove stem; scrape out and discard seeds and veins (see notes). Finely chop chili. Add chili to unwashed pan and stir often over high heat until limp, 1 to 2 minutes. Scrape into one portion of shallot mixture. Add blue cheese to other portion.
Meanwhile, place pretzels in a heavy zip-lock plastic bag and, with a rolling pin, coarsely crush; you should have about 1 cup.
Add 1/3 cup pretzel crumbs and half the cream cheese to each portion of the shallot mixture. Beat with a wooden spoon or an electric mixer on medium speed until blended. Add salt and pepper to taste.
With your hands or a spoon, mound 1 to 1 1/2 teaspoons chili-cream cheese mixture in the cavity of each of half the mushroom caps; mound blue cheese-cream cheese mixture in remaining caps. Arrange each flavor of mushrooms in a 9- by 13-inch baking dish or pan. In a small microwave-safe bowl, melt remaining 2 tablespoons butter in a microwave oven; mix with remaining 1/3 cup pretzel crumbs. Sprinkle over mushrooms, gently pressing into filling.
Bake in a 350° regular or convection oven until mushrooms are well browned, 15 to 20 minutes. With a wide spatula, transfer to a platter. Serve warm.
Nutritional analysis per mushroom.