Peel and finely grate the garlic, finely chop the parsley, stalks and all, then mix both with the soft butter and season with sea salt and black pepper.
Use the tip of a sharp knife to slice into the thickest part of each chicken breast and create a pocket. Divide and stuff in the garlic butter, then shape the breasts back into their original form, sealing the butter inside.
Gather up one sheet of filo in waves and wrap around one breast. Repeat, lining up the kyivs on a large oiled baking tray. Mix 1 tablespoon of olive oil with 1 teaspoon of red wine vinegar, then lightly brush the filo, reserving the remaining mixture for later. Roast on the bottom of the oven for 25 minutes, or until golden, juicy and cooked through.
Meanwhile, chop the potatoes into even-sized chunks and cook in a large pan of boiling salted water for 15 minutes, or until tender, adding the peas for the last 2 minutes.
Trim the tough ends off the broccoli stalks, halve any thicker stalks lengthways, toss with the remaining oil and vinegar mixture and add to the chicken tray for the last 10 minutes.
Drain the potatoes and peas, then mash with 1 teaspoon of extra virgin olive oil and season to perfection. Serve it all together.
