Preheat the oven to 450°F (230°C). Line a large 18 x 13 inch rimmed baking sheet and set it aside.
Trim and discard any tough ends from the broccoli. Cut the stalks into rough chunks and place them in the food processor.
Pulse the stalk pieces in the food processor until they are broken down to a rice-like texture, then spread the processed stalks in a thin layer on the prepared baking sheet.
Cut the broccoli tops into large florets. Pulse the florets in the food processor until they reach a rice-like texture and add them to the baking sheet, mixing with the processed stalks. (If your food processor is very large and powerful, you can process stalks and florets together.)
Drizzle the olive oil and sprinkle the garlic salt evenly over the broccoli rice. Toss with your hands to coat, then spread the mixture into an even, thin layer across the baking sheet.
Roast in the preheated oven for 5 minutes. Remove the sheet, use a large flat spatula to flip and redistribute the rice into a thin layer, then return to the oven and roast for an additional 5 minutes.
Remove from the oven and serve the broccoli rice warm.