Preheat oven to 450 degrees, and line baking sheet with aluminum foil and spread with 1 teaspoon olive oil to prevent sticking.
Remove the main stem of the broccoli, leaving 2 inches of the stem on the florets. Cut each floret in half.
Using a vegetable peeler, peel the outer layer of the stem and cut it into cubes.
Toss the florets, stems and garlic in 1 tablespoon of extra virgin olive oil; spread on the baking sheet, being sure not to crowd the sheet (there should be space between the florets and cubes). Sprinkle with salt and pepper.
Roast for 8 to 15 minutes. Check halfway through, and toss to prevent burning.