Blend the mushrooms in a blade-style spice or coffee grinder until finely ground, about 15 seconds. Remove them from the grinder and sift through a fine mesh sieve into a small bowl to remove any large unground pieces. Transfer 4 teaspoons to a pint-size jar with a lid. Discard any pieces left in the sieve or toss them in your stock pot.
Add the dried garlic to the spice grinder and pulse twice, or until slightly broken but not ground to a fine powder, then transfer to the jar with the mushrooms. Repeat with the dried onions.
Add the salt to the grinder and pulse once, or until broken but not ground to a fine powder. Transfer to the jar along with the sesame seeds, poppy seeds, and nutritional yeast. Screw on the lid and shake to combine. This mixture can be stored in a cool, dry place for up to 3 months.
Whisk together both flours, 3/4 cup everything seasoning, and the baking powder in a large mixing bowl. Add the olive oil and mix with a rubber spatula or wooden spoon. Add the water and stir to combine and create a dough. Turn the dough out onto a floured surface and knead 10 times. Divide the dough into 8 equal pieces, cover with a tea towel, and rest for 15 minutes.
Heat the oven to 450 ℉ with a rack in the middle position.
Lightly flour a work surface and roll out one piece of dough with a rolling pin to a 15" x 5" long strip. Carefully lift and place on one side of a half-sheet pan lined with parchment paper. Repeat with a second piece of dough and place it next to the first piece on the sheet pan. Sprinkle with 1/4 teaspoon of the salt evenly over the entire surface of the doughs.
Bake for 4 minutes then remove from the oven. Carefully flip both pieces over using tongs, rotate the pan, and bake for another 3-4 minutes. Remove from the oven and slide the crackers onto a cooling rack. Repeat the process with all the remaining dough balls using a fresh sheet of parchment and a cool sheet pan.
Break the crackers into pieces and serve as is or with your favorite cracker toppers. Store in airtight containment for up to a week.