Combine 1 cup boiling water and mushrooms in a bowl; cover and let stand 30 minutes or until softened. Drain mushrooms, and finely chop.
Bring 3 cups water to a boil in a large saucepan. Add spaghetti, and cook 20 minutes or until very tender. Drain spaghetti (do not rinse); let cool to room temperature.
Combine spaghetti, mushrooms, breadcrumbs, and next 9 ingredients (breadcrumbs through garlic) in a large bowl; stir well. Divide mixture into 8 equal portions, shaping each into a 3 1/2-inch cake.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 4 cakes, and cook 6 minutes or until golden, turning cakes carefully after 3 minutes. Repeat procedure with remaining oil and cakes. Serve with Asian Black Bean Sauce.