Preheat the oven to 375°F.
Add the rice, salt, olive oil, and 2 cups of water to a saucepan. Bring to a boil, reduce heat to low, cover, and simmer for 20 minutes, or until cooked through. Stir in the parsley.
Pat the salmon dry, season with salt and pepper and arrange on a baking sheet. Cover with lemon slices and roast for 12-15 minutes, until cooked through.
Bring a large pot of salted water to a boil for the broccolini. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the broccolini for 2-4 minutes, until bright green and crisp-tender, then immediately transfer to the ice bath to stop the cooking process. Remove from the ice bath after 1-2 minutes.
To make the aioli, combine all of the ingredients except the oil in a blender until smooth. Drizzle in the oil with the motor running until emulsified. Adjust seasoning.
To serve, divide the rice between plates. Top with salmon and broccolini. Serve with aioli and lemon wedges.