Spatchcock the quails, if your butcher has not done so, by removing the backbone, snipping off the wing tips and flattening the bird with the palm of your hand.
Make the marinade by mixing together all the ingredients in a large bowl. Add the quails and turn to coat, cover and leave in the refrigerator for at least 8 hours but preferably overnight.
Heat a heavy-based frying pan over a medium heat. Cook the quails for 8–10 minutes, turning once and basting regularly with the marinade. Once the quails are cooked through and sticky, remove them from the pan, cover with foil and keep warm.
Heat a clean, nonstick frying pan over a high heat. Toss the sugar snap peas and baby corn in a bowl with the garlic and vegetable oil and then pour into the frying pan. Cook quickly for 2 minutes, moving them occasionally so they don't stick. Return them to the bowl, toss with the sesame oil and soy sauce and serve immediately, topped with the sticky quail and any juices.