In a large bowl, combine ground beef, dillweed, beef base, red onion, salt, pepper, the beaten egg, long grain rice, and 1 cup of olive oil. Mix with your hands or in a stand mixer with the paddle attachment.
Rinse the grape vine leaves thoroughly to remove any salt from the jar and separate the good (large and flat leaves) and set aside. Of those leaves, cut the stems from the base of each leaf as they tend to be stringy and chewy if left on.
Have a large saucepan set aside and ready to fill with dolmades.
Put each rolled dolmade in the pot as you complete it until you run out of meat mixture or the pot is full. Fill the pot until the dolmades are just covered, place a plate upside-down on top of the dolmades (to prevent them from floating), cover with the lid and cook on the stovetop on medium-high heat for 45 minutes. Check one by cutting the center and making sure the meat is cooked through. If they’re still pink on the inside, cook for another 15 minutes.
Allow the dolmades to cool for 10 minutes before serving to ensure they don’t fall apart when you remove them from the pot.
To make the sauce: With a fork, beat the juice from one lemon with ½ cup of olive oil and drizzle it on top of each serving.