Bring a large saucepan of salted water to the boil for the pasta (see cooking tip). Quarter the carrot lengthwise, then thinly slice. Crush or finely chop the garlic. Coarsely chop the olives. Crumble 1 stock cube* into a heatproof jug, add half the tomato paste* and 160ml (⅔ cup) boiling water and stir to dissolve.
Step 2 — Start sauce
Heat a generous drizzle of olive oil in a medium deep frypan over medium-high heat. Cook the carrot, stirring occasionally, for 3-4 mins until softened.
Step 3 — Cook sauce
Add the garlic, half the fennel seeds* and half the chilli flakes* to the carrot and cook, stirring, for 1 min or until fragrant. Stir in the tomatoes, stock mixture, capers, 1 tsp balsamic vinegar and ½ tsp sugar. Season with salt and pepper and bring to the boil. Reduce the heat to medium-high and cook for 5-6 mins until the sauce is slightly reduced.
Step 4 — Cook pasta
While the sauce is cooking, finely grate the parmesan. Add the pasta to the pan of boiling water and cook, stirring to separate the strands, for 3-4 mins until al dente. Reserve 60ml (¼ cup) cooking water, then drain the pasta.
Step 5 — Toss pasta and sauce
Add the pasta and half the parmesan to the sauce. Gradually add the reserved cooking water, stirring constantly, until the sauce coats the pasta and looks slightly glossy. Taste, then season with salt and pepper.
Step 6 — Get ready to serve
Divide the pasta among bowls. Scatter with the olives and remaining parmesan to serve.