In a bowl, cover the nori and the beet with the vinegar and let stand. Toss mushrooms in a mixing bowl and lightly salt. After they begin to release moisture, add the sesame seeds and half of the sesame oil and toss until coated. Let stand.
With a mandoline or vegetable peeler, process the carrots into “noodles” and salt to taste. Do the same with the cucumbers but keep them in separate containers because the liquid strained from the cucumbers is used later in the sauce.
Fold each piece of coconut meat in half and cut perpendicular to the fold, as thin as possible, so that the pieces look like noodles. (Coconut is an optional ingredient in this dish; don’t be discouraged if you can’t find it or make it look like vermicelli.) Strain the cucumbers and set aside 5 ounces of the liquid.
To make the sauce, remove the beet from the vinegar and discard it. Blend the vinegar and nori with the agave nectar, ginger and cucumber liquid. Stir in the remaining sesame oil and more salt, if desired.
Assemble the dish in soup bowls, with the coconut on the bottom of each bowl. Top the coconut with equal-size mounds of cucumber and carrot, and torn leaves of cilantro and basil. Lay the mushrooms in the center, on top of the herbs and vegetables. Stir the sauce well before ladling it over each serving. Garnish with almonds and a sprinkle of crushed red pepper.