Prep the beets. Scrub the beets clean. Using a vegetable peeler, peel the golden beets first, then the red beets to avoid color transfer. Slice them into wedges about ¾–1 inch (2–2.5 cm) at the widest part.
Roast the beets. Transfer the beets to a sheet pan. Add 2 tbsp olive oil, ½ tsp salt, and ⅛ tsp black pepper. Toss well with your hands until evenly coated. Arrange the beets cut side down in a single layer and bake at 425°F (220°C) on the middle rack for 10 minutes.
Prep the carrots. While the beets roast, scrub and peel the carrots. Roll-cut them into ¾–1-inch sections at the widest part.
Make the sesame dressing (see details below). While the beets are in the oven, toast sesame seeds until fragrant and golden. Combine them with mayo, rice vinegar, soy sauce, sesame oil, mirin, and sugar. Whisk until smooth. For a thicker or deeper flavor, add tahini or shiitake seasoning. (See the How to Make the Sesame Dressing section below for full details.)
Add the carrots. Remove the sheet pan and flip the beets so the other side touches the pan. Push the beets to one side, then add the carrots. Drizzle with 1 tbsp olive oil, ¼ tsp salt, and a light sprinkle of pepper. Carefully use your hands to coat evenly (the pan will be hot).
Roast until tender. Return the pan to the oven and bake for 15–20 minutes (I baked for 20 minutes but checked at 15).
Check for doneness: After roasting, pierce a beet with a fork or chopstick. If it goes in easily, they’re done. For a softer texture, roast for 5 more minutes. (I added 5 extra minutes for a soft yet slightly firm bite.)
Serve. Transfer everything to a large serving plate. Just before serving, drizzle with a few tablespoons of sesame dressing, garnish with scallions, and squeeze fresh lime juice over. Serve warm.
Notes
How to Make the Sesame Dressing
In a dry cast-iron skillet, lightly toast the sesame seeds over low heat, shaking the pan often until fragrant and light to medium brown, about 5 minutes.
Transfer the toasted seeds to a mortar and pestle (or a clean coffee grinder) and grind coarsely. Place them in a large measuring cup.
Add the remaining ingredients from mayo to brown sugar. Whisk until smooth and no lumps remain.
Taste and adjust. For a thicker consistency, stir in 1–2 tsp tahini. For deeper umami flavor, add the shiitake mushroom seasoning.
Wear food-handling gloves to prevent staining your hands.
Use a dark-colored cutting board (avoid wooden boards, which absorb color) to prevent staining.
Make-ahead (dressing): The dressing will keep for up to 1 week in the fridge; when ready to use, shake well and thin with a little water if it’s thick.
Make-ahead (beets): Roast the beets ahead of time and store them separately (so the red and golden don’t bleed into each other). You can roast them 1–2 days ahead and then re-warm by spreading on a sheet pan and baking at 380 °F (≈ 190 °C) for about 10 minutes.
Storage (roasted beets): After roasting and cooling, store in an airtight container in the refrigerator. Cooked beets generally keep for about 3–4 days when properly stored.
Storage (dressing): Keep the dressing refrigerated in a sealed container; use within 1 week for best flavour and texture.