Preheat the oven to 200°C, fan 180°C, gas mark 6.
Put the vegetables into a roasting tray, scatter with the thyme, season well and drizzle over 2 tablespoons of the olive oil. Roast for 35 minutes or until softened and lightly charred.
Make the pesto: whiz together the garlic, basil, pine nuts, Parmesan, and chilli, with 4 tablespoons of olive oil in a food processor (or mix in a pestle and mortar). Season and set aside.
Heat a griddle pan. Season the lamb and rub in some of the remaining oil, but be careful not to use too much as it will make the griddle smoke.
Cook the lamb for about 2-3 minutes each side until just cooked through but still pink in the centre (exact timings will depend on the thickness of the steaks). Wrap in foil and allow to rest for a few minutes.
Allow the veg to cool slightly, add a squeeze of lemon juice, mix through the leaves and crumble in the feta.
Serve the vegetables with the lamb and spoon over the pesto.