Peel and slice carrots lengthwise and line bottom of pot with them. This helps keep the grape leaves from sticking to the pot.
Soak rice in hot water for 10 minutes and drain. In a large bowl, combine rice, beef, onion, garlic, tomato sauce, tomato paste, and all spices.
Place each grape leaf shiny side down with stem end toward you on a flat surface. Cut off stem. Place 1 tbsp of rice mixture on leaf near the stem end. Roll top over once, fold ends in, and continue to roll completely (rolling away from you). Repeat with remaining leaves.
Arrange rolled grape leaves in pot seam side down, tightly packed. Place each layer in opposite direction of previous layer, in a criss-cross fashion. For even cooking, try to have no more than 4 layers.
Combine lemon juice and oil and pour over grape leaves. Top with water until approximately 1" below top layer.
Place large plate on top, and place a heavy weight on plate (a foil-wrapped brick works great).
Bring to a boil, then reduce heat to low and simmer for 1 hour 15 minutes to 1 hour 30 minutes, until rice is thoroughly cooked. Allow to rest for 20-30 minutes.