Preheat your oven on to 400°F (200°C), or 180°C if you have a fan oven, and line a half size rimmed sheet pan with parchment paper or silicone baking mat for easy cleanup.
Wash the broccoli, drain, and cut it into small, bite-sized florets. Wash the carrots, peel, and cut into ½ inch pieces.
Place the broccoli and carrots on the prepared sheet pan. Drizzle olive oil and season with salt and pepper. Mix well and spread it out evenly. Bake for 15 minutes.
Take the pan out and flip the broccoli and carrots. Return to the oven for another 10 minutes but keep an eye on the broccoli so it doesn’t burn, you want the ends lightly charred.
In a bowl or a jar, combine extra virgin olive oil, fresh lemon juice, honey, dijon mustard, finely diced shallot, ground black pepper, and salt. Whisk or shake the jar until the dressing is well combined and creamy.
Remove the broccoli and carrots from the oven and pour the vinaigrette over it. Toss to combine, and serve.