Preheat oven to 425°F (220°C).
Wrap beets individually in foil with a small drizzle of olive oil and a pinch of salt. Place on a baking sheet.
Roast until tender when pierced, about 45–60 minutes depending on size. Cool slightly, then rub off skins with a paper towel. Cut into wedges or 1-inch chunks.
Toss carrots with 2 tablespoons olive oil, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1 teaspoon honey if using.
Spread on a separate sheet pan. Roast at 425°F until caramelized and tender, about 20–25 minutes, tossing once.
In a small jar, combine olive oil, lemon juice, orange juice, Dijon, honey, salt, and pepper.
Seal and shake until emulsified. Taste and adjust seasoning. You want bright, a little sweet, and well-salted.
In a large bowl, toss warm roasted beets and carrots with half the vinaigrette.
Add arugula and gently fold with a bit more dressing until lightly coated.
Transfer to a platter. Tear burrata over the top, letting the creamy center spill out.
Finish with toasted nuts, orange zest, a drizzle of remaining vinaigrette, and a pinch of flaky sea salt.
Roast beets separately: They can stain carrots. Keep them on different pans until tossing with dressing.
Use warm vegetables: Warm beets and carrots slightly melt the burrata and soak up the dressing.
Salt in layers: Season the vegetables, the dressing, and the final salad for deeper flavor.
Don’t drown it: Add dressing gradually. You can always add more at the table.