Spread the puffballs out on a non-stick baking sheet and cook at 275 for 30-45 minutes, or until toasty brown and completely cooked.
Squeeze the puffballs chunks a bit to compress them (this should end up being around 2 packed cups), then place in the bowl of a food processor (or a highspeed blender like I use in the pictures, which will give the smoothest result).
Add the garlic, lemon, cumin, salt, tahini, and water and puree the mixture until smooth, then start drizzling in the oils slowly like you're making mayonnaise, which is the key to making the velvety-smooth hummus pictured. If the mixture seems difficult to purée, add a splash of lemon or water until the blades of the processor move. Use your instinct to make a smooth purée.
When all the oil has been added, double check the seasoning for salt and lemon, adjust as needed, then transfer to a labeled, dated container and refrigerate until needed.
Notes
Improvising
If you don't have a highspeed blender, use a food processor, just be patient and drizzle in the oil slowly to make a thick puree. You may need to add a splash of water to help it come together.