Remove the membrane from the back of each rack of ribs by slipping a knife under it and pulling it away. This step is crucial for allowing the dry rub to penetrate the meat.
In a bowl, combine paprika, garlic powder, onion powder, black pepper, ground mustard, brown sugar, celery salt, dried oregano, dried thyme, cayenne pepper, and kosher salt. Mix well.
Generously coat both sides of the ribs with the dry rub. Use your hands to press the rub into the meat, ensuring it's fully covered. Let the ribs sit with the rub on them for at least 30 minutes, or refrigerate overnight for deeper flavor.
Preheat your oven to 275°F (135°C).
Wrap each rack of ribs tightly in aluminum foil. Place the wrapped ribs on a baking sheet or directly on the oven racks.
Bake in the preheated oven for about 2.5 to 3 hours, or until the meat is very tender and pulls away from the bones.
Carefully remove the ribs from the foil and place them back on the baking sheet, bone-side down. Broil for a few minutes until the outside gets a bit crispy and the rub forms a crust.
Let the ribs rest for about 10 minutes before slicing into individual ribs. Serve them hot with sides of your choice, like coleslaw or cornbread, for a true Memphis-style feast.