First we got the R56 on the lift, removed the new Rota wheels. These are the factory brakes you see here, adequate for the average user. The biggest problem with the factory pads is the ridiculous amounts of dust they throw off. If nothing else, we would recommend aftermarket pads for that reason alone.
While the stock brakes on our long term MINI Cooper S were more than adequate for daily driving, we felt we could use a little extra stopping power for the canyon driving and occasional track use the car sees. We didn't want to go all the way with a big brake kit, as we wanted to stay with 17-inch wheels. We also wanted to see what we could do at minimal cost and effort.
After talking to the experts at Stoptech Brakes, we determined that their stage 2 would be exactly what we were looking for. The kit consists of Stoptech cross-drilled rotors, Hawk street pads, stainless steel brake lines and Motul RBF600 fluid. Since the car is used mostly for street driving we weren't as concerned with the cross drilled rotors as we would have been if it were a dedicated track car. For the same reason, we also chose the Hawk street performance pad. We wanted a pad that would respond well when cold, be low dust and had fittings for the factory brake wear sensors. The only downside to the Hawk pads is noise. The stock pad has an anti-vibration shim riveted to the backing plate that the Hawks lack. The extra vibration results in squeal, which is slight, but still very much present. We are looking at various solutions including backing plates to solve the problem.
Loosen bolt that locates the brake disc. It may be rather stubborn and require a little force. Once broken loose, leave it in place to hold the disc on until ready for removal, this can save some broken toes. | 
Remove bolts that hold the caliper to the carrier. Removing the bottom first is easiest, as caliper won't swing down. This step will usually require two wrenches. |
Start by loosening the wire to the factory brake pad wear sensor. We chose pads, which still utilize these sensors, if you chose a pad without sensors this wire will need to be relocated. | |
We took the MINI to the guys at Evosport in Huntington Beach California to have the new brake kit installed. Evosport has been building racecars and high performance street cars since 1999 and while this job may seem a little mundane, it was finished with the same level of excellence they apply to everything they do. This can easily be done by your average weekend mechanic in a driveway with basic hand tools, but if you don't feel comfortable take it to a pro, these are your brakes after all.
Hang the caliper from the strut using a coat hanger, then remover caliper carrier by removing the two bolts in the back. | 
It now safe to remove the rotor locating bolt and remove the rotor. Ours fell off in our hands, others may need a little encouragement to release from the hub. |
If changing brake-lines at the same time, now is a good time. It is helpful to have a plug or cap for the factory brake lines here. We used an old section of brake line that had been capped off. Warning, brake fluid is an excellent paint stripper, be very careful not to let it touch anything. | 
Reinstall rotor, carrier, pads and caliper in the reverse of how they came off. A little anti-seize compound on the hubs and rotor-locating bolt will help the next time you do this job. |
Install the new braided brake lines being careful not to cross thread them or damage the ends. There is no torque spec here, so it is necessary to go by feel. | 
Everything installed and cleaned up. It is important to clean everything off before bedding in the rotors; any contaminants in the system can ruin the procedure. |