Cut the cabbage in half, then carefully cut out the core. Cut it into half again so that you have quarters, then slice the cabbage into ultra-thin ribbons. You will have 10 to 12 cups total. Place it in a very large bowl.
Cut off the four sides of the apple, slicing as close to the core as possible. Discard the core, then cut the remaining quarters into thin slices. Add the apples to the bowl with the cabbage.
In a small mixing bowl or a larger liquid measuring cup, whisk together the lemon juice, olive oil, salt, and pepper. Pour over the cabbage and toss to combine. Sprinkle with the dried cranberries, pumpkin seeds, and Parmesan. If time allows, let sit for 15 minutes. Toss and adjust seasoning as desired.
This slaw lasts in the refrigerator for up to 5 days, so you can make it well in advance too! Taste and adjust the seasoning before serving.