Cook the pasta according to the packet instructions.
Peel the garlic and place in a blender with the olives, half the thyme leaves, 1 teaspoon of black pepper, 6 tablespoons of olive oil and the balsamic. Blitz until super-smooth.
Drain the pasta, reserving a mugful of starchy cooking water, then return it to the pan.
Pour over half the olive sauce (save the rest in the fridge for up to 3 days, or freeze in an ice cube tray for future meals) and toss together, loosening with a splash of cooking water, if needed.
Divide between serving plates, drizzle with 1 tablespoon of extra virgin olive oil, crumble over the feta and pick over the remaining thyme, then thinly slice and scatter over a few extra olives, to finish.
