To make applesauce: In a large stockpot, combine all the ingredients and heat over medium-low heat, stirring frequently until soft, about 20 minutes.
When the apples are tender, turn off the heat, and gently mash them with a wooden spoon to the desired consistency. This applesauce is delicious warm or cold.
To make the latkes: Grate the potatoes and place them in a large bowl. Add the onions and toss together.
Take a large handful of potato-onion mixture and squeeze to remove excess water. Pile the mixture onto paper towels. Repeat with the rest of the mixture, changing paper towels if needed. Return the mixture to the dry bowl.
In a separate bowl, lightly beat the eggs. Pour the eggs into the potato-onion mixture, and stir, gradually adding the matzo meal. Add the salt and pepper.
Pour ¾ inch of oil into a 10- to 12-inch frying pan with sides at least 2 inches high, and heat over medium-high heat for 3 to 4 minutes. Form the batter into thin, palm-sized patties, and carefully place them in the frying pan, 4 patties at a time. Flip your latkes when the bottoms are golden brown. This usually takes 3 to 4 minutes.
When the latkes are browned on both sides, place them on paper towels to absorb excess oil, and continue this process with the remaining batter.
Serve hot, with sour cream and applesauce.