Clean the mushrooms with a soft cloth. To enhance the flavor slightly, dehydrate the mushrooms for an hour or two. This is optional. To enjoy the fresher tasting version, just skip the dehydrating step.
In a blender, puree the red pepper until liquefied, adding water as needed for blending. Stir together with the ground flax seeds and let the flax seeds soak in this for 15 minutes or so, until the flax seeds have become gooey. This is what will hold the burgers together.
In a food processor fitted with an "S" blade, pulse the mushrooms, walnuts, jalapeno, onion, and celery until chopped finely. Stir in the red pepper and flax mixture and two tablespoons olive oil.
Form burgers and place on a teflex or plastic sheet. Spread just a bit of olive oil on your sheets so the burgers will flip easily, if needed. Dehydrate for about 2 hours then flip onto a regular dehydrator screen and let finish dehydrating, which takes about another 2 hours.
The avocado mayo is simple. Just blend the avocado, agave, vinegar and spices until creamy. A blender will make this nice and creamy, but mashing with a fork would probably suffice.
Serve the burgers on a bed of lettuce leaves, with a dollop of avocado mayo, some chopped red onion, and chopped jalapenos.