Preheat water to 134°F using a sous vide machine. (I use the Anova sous vide precision cooker.)
Prepare lamb chops by rinsing under cold water. Pat dry with paper towels and set them aside. Season the lamb chops with salt, pepper, cumin, and cayenne pepper. Set aside.
Heat a cast-iron skillet over medium-high heat for 3-5 minutes. Add olive oil into the skillet and swirl to coat the bottom. Place rosemary sprigs and garlic cloves into the skillet. Pre-sear the lamb chops on both sides, about 30 seconds per side.
Prepare two sous vide bags and place 4 lamb chops into each bag. Transfer the rosemary and garlic from the skillet to the sous vide bags. Add lemon slices if using. Vacuum seal them with a hand pump or a vacuum sealer.
Lower the sealed bags into the preheated water bath, making sure the lamb is under the waterline. Set the timer for 2 hours.
Once the timer goes off, remove the bags from the water bath and remove the lamb from the bags onto a plate. Pat dry with paper towels. Reserve the lamb juice for the broccoli.
Heat up the same skillet, use the leftover oil in the skillet to sear the lamb chops on both sides, about 30 seconds per side until well-browned. Transfer to serving plates and let the lamb chops rest for 5 minutes.
In the meanwhile, make the broccoli. Still in the same skillet (if it’s big enough), heat olive oil over medium-high heat. Add garlic and stir until fragrant, about 30 seconds.
Place broccoli florets in the skillet; sauté for about a minute.
Pour the reserved lamb juice over the broccoli and cover to steam for 5 minutes or until the broccoli is tender. (Your lamb juice should be flavorful enough for the broccoli. Taste after cooking, and if desired, add a pinch of salt and mix well.)
Serve the lamb chops with the steamed broccoli. Enjoy!