Preheat the oven to its highest temperature with a rack in the centre.
Heat 30ml oil in a heavy ovenproof pan over high heat until lightly smoking.
Add carrots and salt, tossing to coat thoroughly.
Sear carrots for 6 to 8 minutes until browned in spots.
Roast in the oven for 8 to 12 minutes until tender, then cool slightly.
Toss 40g carrot tops and basil leaves in a bowl.
Whisk 30ml oil with lemon juice and salt for the dressing.
Pulse carrot tops and basil in a food processor for the pesto.
Add walnuts, Parmesan, garlic, and salt, then pulse again.
Slowly blend in 110ml oil until the pesto is combined but chunky.
Arrange burrata and carrots on a platter and top with pesto and garnish.