Rinse the chicken legs and pat dry. Pluck the leaves from the sage, rosemary, and parsley sprigs and chop finely. Wash the lemon with hot water, pat dry, then grate the zest and squeeze the juice. Peel the garlic and dice finely (or use a garlic press).
In a bowl, combine the chopped herbs, garlic, lemon juice, lemon zest, and mustard to form a paste.
Lift the skin at the edges of each chicken drumstick, loosening with a small kitchen knife if necessary. Push the herb paste under the skin and spread evenly using your fingers.
Refrigerate the prepared chicken legs for 1 hour to allow the flavors to infuse.
Brush the chicken legs with olive oil and season with salt and pepper. Grill skin-side down over medium-low heat for 20 minutes. Turn and grill for 10-15 minutes. Turn again and grill for 5 minutes until the internal temperature reaches 74°C (165°F).
Alternatively, brush the chicken with olive oil, season with salt and pepper, and broil in the oven until the internal temperature reaches 74°C (165°F).