Place quartered apples in a large stainless steel or enamel stock pot (not aluminum), add water halfway up apples, and cook over medium heat for 25-30 minutes or until apples are super soft and mushy. Let cool for 15 minutes or so.
If also making jelly, carefully pour apples and juice into a large fine mesh strainer over another pot or large bowl. Let sit for several hours, until no longer dripping into pot.
Put drained apples through a food mill or smash through a small-holed colander until all the pulp is separated from the skins and seeds.
Measure the pulp into a stainless steel pot. Add sugar, vinegar, lemon juice, and spices.
Bring just to a low boil then reduce heat to a simmer and cook, stirring, for about 15 minutes. If too liquidy, continue cooking until thicker. If it's too thick, add a small amount of saved juice or water.
Ladle the hot apple butter into hot jars, leaving 1/2-inch head space, if canning. Put on hot, sterile lids and screw on rings. Process pints 10 minutes or 1/2 pints 5 minutes in boiling water bath. When cool, test for seal.
If freezing, ladle into wide-mouthed glass containers leaving a 1/2" head space and let cool before putting on lids. (Jars with no shoulder.)
Store in the freezer for up to a year. Let thaw in the refrigerator to use.