Place approximately 2 pounds beef fat trimmings in a single layer on a cookie sheet. Freeze for approximately 2 hours or until very stiff, but not completely frozen through.
Dice the trimmings as fine as possible to get the best yield. Alternatively, run the partially frozen fat through a chilled meat grinder.
Note: If you are not buying large amounts of beef at a time, keep a bag in your freezer and keep adding to it until you have a couple pounds or more of diced trimmings.
Add the trimmings to a slow cooker and cook on low for 6 to 8 hours, stirring every once in a while. Keep things low and slow so that it doesn't burn.
Once the fat has finished rendering, strain it through an ultra-fine meshed cheesecloth or strainer. It is important to use an ultra-fine mesh to strain out impurities (protein) that will cause the tallow to mold over time.
Tallow may be kept at in an airtight container in a cool, dark place for a couple months, but will last longer in the refrigerator and even longer if frozen. If freezing, consider using ice cube molds to portion out the tallow.
Yields approximately 1/2 to 3/4 cup tallow from 1 pound beef fat trimmings.
Notes
If you'd like, you can create cracklings from the leftover solids.