Combine sugar and lemon verbena leaves in the bowl of a food processor; pulse until the leaves are fully incorporated in the sugar (the sugar will become light green).
Combine sugar-lemon verbena mixture and apricots in a large bowl. Cover and marinate in the fridge for 4 hours.
Inspect 4 jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until jam is ready. Wash new, unused lids and rings in warm soapy water.
Transfer apricot-sugar mixture to a large pot and stir in pectin. Slowly bring to a full rolling boil that does not stop bubbling when stirred. Cook for 1 minute, stirring constantly.
Ladle apricot jam into the prepared jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any spills. Top with lids and tightly screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 10 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart. Let rest for 24 hours without moving the jars. Gently press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area.
