Preheat the oven to 220°C, fan 200°C, gas 7. Unroll the puff pastry, leaving it on its parchment paper, and place it on a large baking sheet. Score a 1.5cm border with a sharp knife, being careful not to cut all the way through. With a fork, prick the inside all around. Preheat oven to 350°F and bake for 15 minutes.
Gently press down the center of the pastry where it has risen with a fork. Spread the chutney on top, then distribute the beets and crumble the salad cheese on top. Season lightly, then bake for another 8-10 minutes, or until the dough is golden and the feta has lightened in color.
Meanwhile, prepare the couscous according to the package directions. Season with salt and pepper and stir in the spinach to wilt it slightly. Add one-third of the parsley.
Remove the tart from the oven and, if desired, drizzle with a little olive oil before scattering the remaining parsley on top. Serve with the couscous salad, cut into four pieces.