Place the oil in a pan on medium-low heat.
Make a slit in the tofu container and drain out the water in the sink. Then gently squeeze the container to get out any excess liquid. Take the block of tofu out of the container and place it on a cutting board. Cut 1/8-inch slices along the short side. Turn the cutting board and cut two slices along the long side of the tofu, making 36 or so 1 1/2-inch by 2-inch pieces.
Lay out each piece of tofu in the hot pan. Pour on the dressing and sprinkle on the minced ginger, cumin, salt, and pepper. Allow to cook for 15 to 20 minutes or until the bottom of each piece is slightly browned. Flip pieces as they're ready and lightly brown the other side. Set aside to cool.
While the tofu is cooking, prepare the cucumbers. Using a mandolin slicer or a regular knife, cut the cucumber lengthwise in 1/8-inch-thick slices. You should get eight slices out of the cucumber.
Lay one cucumber slice flat on the cutting board. Place a stack of four pieces of tofu on one end of the cucumber, roll it up, and place a toothpick through the center to keep it in a tight roll. Repeat until you make eight cucumber tofu rolls (two servings). Enjoy immediately.