Bring a medium saucepan of salted water to the boil for the spaghetti. Finely chop the carrot and onion. Crush or finely chop the garlic. Coarsely grate the zucchini. Finely chop the thyme leaves, discarding the tough stems. Crumble 1 stock cube* into a heatproof jug, add 250ml (1 cup) boiling water and stir to dissolve.
Step 2 — Brown lamb mince
Heat 1 tsp olive oil in a large frypan over medium-high heat. Cook the lamb mince, breaking up the lumps with a spoon, for 3-4 mins until browned. Season with salt and pepper, then remove from the pan.
Step 3 — Cook vegetables
Reduce the heat to medium, add the carrot, onion and garlic to the same pan and cook, stirring regularly, for 3-5 mins until softened.
Step 4 — Cook spaghetti
While the vegetables are cooking, cook three-quarters of the spaghetti* in the pan of boiling water for 12 mins or until al dente. Drain. Return the spaghetti to the pan.
Step 5 — Simmer sauce
Add the tomato paste to the vegetable mixture and cook, stirring, for 1 min. Add the mince, thyme, stock, ½ tsp sugar and a pinch of chilli flakes (chilli is not essential to the dish; you can omit it). Bring to a simmer and cook, stirring occasionally, for 6 mins or until slightly thickened. Taste, then season with salt and pepper.
Step 6 — Get ready to serve
Meanwhile, finely grate the parmesan. Add the zucchini and sauce to the spaghetti and and toss to combine. Divide the spaghetti mixture among bowls. Scatter over the parmesan and serve with the remaining chilli flakes, if desired.