Preheat oven to 425 degrees. On a large rimmed baking sheet, toss mushrooms with oil and 2/3 cup water; season with salt and pepper. Arrange stemmed side down; cover loosely with foil. Roast until tender, 30 to 45 minutes.
Meanwhile, in a medium mixing bowl, mash avocado with a fork. Stir in mustard, horseradish, and lime juice. Fold in jalapeno season with salt and pepper.
Toast rolls. Dividing evenly, layer each bottom half with tomato and portobello, and each top half with avocado mixture.