Preheat the oven to 400°. On a large baking sheet, toss the broccoli florets and stems with 2 tablespoons of the olive oil and season with salt and pepper. Roast the broccoli in the oven for about 30 minutes, tossing halfway through, until browned and tender.
In a small bowl, whisk the lemon juice with the shallot and the remaining 2 tablespoons of olive oil and season with salt and pepper. Scrape the broccoli into a bowl. Add the dressing, walnuts and goat cheese, toss well and serve.