Smash celery into juicy bits using a mortar and pestle. Combine with ground beef in a large bowl. Add garlic powder, paprika, mustard seeds, kosher salt, black pepper, cayenne pepper, curing salt, and sugar. Mix by hand until thoroughly combined.
Transfer meat onto a large piece of parchment paper. Use damp hands to shape into a 4-inch-thick log. Roll up in the parchment paper, compressing it as much as possible. Twist ends tightly to seal. Place on a paper towel-lined baking sheet and refrigerate for 24 hours.
Preheat the oven to 275 degrees F (135 degrees C).
Cut ends off the parchment paper and unwrap meat. Mix liquid smoke with water and generously brush over meat. Roll meat back up in the paper, then again in aluminum foil, sealing it tightly and twisting the ends in opposite directions.
Line a baking sheet with a wire rack and place sealed meat on top. Poke 5 or 6 holes across bottom for excess moisture to drip out.
Bake in the preheated oven until the internal temperature reaches 150 degrees F (66 degrees C) and no higher, about 1 1/2 hours.
Let sausage cool in the pan until room temperature, at least 30 minutes. Give ends a tighter twist, then refrigerate at least 8 hours, or overnight.
Unwrap sausage and slice in half. Coat outsides with freshly ground black pepper, place on a plate lined with crinkled foil, and let dry in the refrigerator for 24 hours.