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Cut each rib rack in half between 2 center bones.
Combine 3 quarts cold water, ¾ cup salt, sugar, and liquid smoke in stockpot or large plastic container and whisk until sugar is dissolved.
Add ribs, pressing to submerge. Cover with plastic wrap and refrigerate for at least 1 hour or up to 4 hours.
Adjust oven rack to middle position and heat oven to 275 degrees.
Line rimmed baking sheet with aluminum foil and set wire rack in sheet.
Combine salt, pepper, garlic, and cayenne in small bowl.
Remove ribs from brine. Pat dry with paper towels and sprinkle ribs all over with pepper mixture.
Place ribs meat side up on prepared wire rack. Roast for 2½ hours.
Meanwhile, heat oil in medium saucepan over medium heat until just shimmering.
Add onion and cook until softened, about 5 minutes.
Stir in ketchup, vinegar, sugar, Worcestershire, pepper, liquid smoke, and cumin.
Bring to boil and cook until slightly thickened, about 4 minutes; set aside off heat.
Brush meat sides of ribs with ¼ cup sauce.
Return to oven and continue to roast until tender and fork inserted into meat meets little resistance, 2 to 2½ hours longer.
Remove from oven and brush meat side of ribs with additional ¼ cup sauce.
Tent with foil and let rest for 30 minutes.
Cut ribs between bones and serve, passing remaining barbecue sauce separately.