Combine cranberries, white sugar, turbinado sugar, water, orange zest, cinnamon, ginger, cloves, allspice, and pepper in a large pot over medium heat. Simmer, stirring frequently, until sugar dissolves and cranberries pop, 10 to 12 minutes.

Blend cranberry jam into desired consistency using an immersion blender.

Pour jam into a glass pint jar; cool until thickened and set, about 1 hour. Seal jar and refrigerate.