Heat the oven to 200°F. Rinse and core the apples; peel them if you’d like and chop them into 1-inch chunks. Put them in a small saucepan along with 1/4 cup of water, the cranberries, sugar, and cinnamon stick. Cook, stirring frequently until the fruit begins to soften and break apart, 15 to 20 minutes; remove the pan from the heat.
Line a colander with a clean kitchen towel. Scrub and peel the potatoes; grate them by hand or with the grating disk of a food processor (by hand will take longer). Drain the potatoes in the prepared colander, pressing down to extract excess water; transfer them to a large mixing bowl. Rinse and trim the zucchini; grate it the same way as the potatoes, but don’t bother to drain it
(there’s no need to wash the bowl of the food processor or grater between uses); add the zucchini to the bowl. Trim, peel, and grate the onion; add it to the bowl along with the chickpea flour. Sprinkle generously with salt and pepper and mix well with your hands.
Rinse and halve the lemon. Wash the bowl of the food processor and fit it with the metal blade. Put half the tofu in the bowl and squeeze in the juice from one half lemon (refrigerate the remaining tofu and lemon in airtight containers for another use, like adding to soup or scrambling with cooked vegetables). Pulse until the mixture is smooth and transfer it to a small bowl. Taste, sprinkle with salt, and stir in the poppy seeds.
Line a plate with paper towels. Put 1 tablespoon oil in a large skillet (preferably cast iron or nonstick) over medium-high heat. When it’s hot, drop the potato batter into it by the 1/4 cup or large spoonful, using the back of the utensil to spread it out into a thin layer. Cook, working in batches so the pan isn’t overcrowded, until the pancakes are browned on the bottom, 3 to 5 minutes. Turn the pancakes and cook until they’re browned on the other side, 3 to 5 minutes more. Transfer to the paper towels to drain and sprinkle with salt. Transfer the pancakes to an ovenproof plate and put the plate in the oven. Repeat with the remaining batter, adding the remaining 1 tablespoon oil as needed between batches.
Serve the latkes with the cran-apple compote and poppy-seed sour cream.