Preheat Oven and Prep Pan: Preheat oven to 425 °F (218 °C). Line a rimmed baking sheet with parchment paper.
Toss and Season Vegetables: Place broccoli and carrots in a large bowl; drizzle with olive oil, sprinkle with thyme leaves and season to taste with salt and pepper; toss well to coat.
Roast for Crispness: Spread in an even layer on the prepared baking sheet; bake until tender and nicely browned (20 to 25 minutes), stirring once halfway through.
Finish with Brightness: Transfer to serving bowl and add lemon juice and parsley; toss to combine. Season to taste with salt and pepper; serve.
Notes
For Even Cooking: Slice carrots slightly smaller than broccoli florets to be sure that both the dense carrots and the delicate broccoli cook perfectly at the same rate.
Easy Cleanup: Line your baking sheet with parchment paper to prevents sticking and make cleanup simple.
Fresh Herbs: Fresh thyme and parsley are best. If you use dried thyme, use half the amount and stir it into the olive oil before tossing with the vegetables.