Preheat oven to 400 degrees F. Spread broccoli florets and quartered shallots onto a parchment paper-lined baking sheet. Drizzle with 2 Tbsp olive oil, salt, and pepper, tossing to coat. Bake for 30 minutes, turning veggies over after 15 minutes to evenly cook.
Meanwhile, set a small saute pan over medium heat and add the pinenuts. Cook until lightly browned and toasted, then remove from heat.
Whisk together 1 Tbsp olive oil, lemon juice, and basil leaves. Sprinkle over the roasted veggies along with the pinenuts and goats cheese, then toss to mix. Serve warm or cold as a salad or side dish!