Coarsely grate the carrot. Finely chop the thyme leaves, discarding the tough stems. Finely chop the garlic, then using the flat side of the knife, mash to a paste (adding a little salt to the garlic on the chopping board helps). Finely grate the parmesan. Crumble 1 stock cube* into a heatproof jug, add 180ml (¾ cup) boiling water and stir to dissolve.
Step 2 — Start sauce
Bring a medium saucepan of salted water to the boil for the pasta. Heat 1 tbs olive oil in a medium deep frypan over medium-high heat. Add the carrot, thyme and two-thirds of the garlic and cook, stirring occasionally, for 3-4 mins until softened.
Step 3 — Simmer sauce
Add the beef mince to the carrot mixture and cook, breaking up the lumps with a spoon, for 3-4 mins until browned. Stir in the tomatoes, stock and ½ tsp sugar and season with salt and pepper, then bring to a simmer. Reduce the heat to medium and cook, stirring occasionally, for 10-12 mins until slightly thickened.
Step 4 — Cook pasta and sauce
Meanwhile, cook the pasta in the pan of boiling water for 10 mins or until al dente. Reserve 80ml (⅓ cup) cooking water, then drain the pasta. Add the pasta, reserved cooking water and half the parmesan to the sauce and stir well to combine. Taste, then season with salt and pepper. Remove from the heat.
Step 5 — Make gremolata drizzle
While the pasta is cooking, finely chop the parsley leaves, discarding the stems. Finely grate the zest of half the lemon*, then juice the half. Combine the parsley, lemon zest, remaining garlic and 1 tbs extra virgin olive oil in a bowl and season with salt and pepper.
Step 6 — Dress rocket and serve
Combine 1 tsp lemon juice*, 2 tsp extra virgin olive oil, ½ tsp dijon mustard and ¼ tsp honey in a large bowl and season with salt and pepper. Add the rocket to the dressing and gently toss to coat. Divide the pasta among bowls. Drizzle with the gremolata and scatter with the remaining parmesan. Serve with the dressed rocket.