Cut 4 pencil-long and equally thick sticks from twigs and peel off the bark.
Flatten the meat and bacon if necessary.
Season the meat well with salt, pepper and thyme and place the bacon slices on top. Coat the 4 sticks with oil, wrap them tightly with the meat and pin the meat or wrap with kitchen twine. Brush with oil and grill slowly on charcoal grill for about 20 minutes.
Turn occasionally. Serve with herb mayonnaise, if desired.