Preheat the oven to 425 degrees. Spray a sheet pan with vegetable spray and set aside.
Prepare the jerusalem artichokes first. Squeeze the lemon into a medium bowl and add the water - this acidulated water will prevent the artichokes from oxidizing. Peel the artichokes with a vegetable peeler and cut into bite sized pieces. Immediately transfer to the water.
Prepare the rest of the vegetables and transfer to the sheet pan.
In a small bowl combine the garlic, rosemary, salt and pepper. Remove the artichokes from the water and pat dry with a clean towel. Add them to the other vegetables. Drizzle the vegetables with olive oil and sprinkle on the rosemary mixture. Use your hands to to coat the vegetables with olive oil and herb mix. When they are coated, arrange the vegetables so that the cut side of the brussel sprouts and potatoes are on the cookie sheet. Spread the rest of the vegetables out in an even layer.
Roast for 25-30 minutes, then use a metal spatula to flip the vegetables over. Continue roasting for another 10-15 minutes or until golden brown and fragrant.