Cut the apples and pears off the core and then chop into pieces. If desired you can peel the apples and pears before cutting them off the core.
Place the apples and pears in a large saucepan along with the sugar, lemon juice, cinnamon, and nutmeg.
Heat over medium hight heat, stirring frequently, until the mixture begins to boil. Reduce heat to medium low and simmer for 10-15 minutes.
Take a potato masher and mash the mixture until it is fairly smooth. It will still have some chunks in it. If you like a smoother applesauce you can place it in a food processor and process until smooth.
Remove the mixture from the heat and add the vanilla bean paste. Mix well.
Cool completely and then store in the refrigerator for up to 5 days.