In a small saucepan, cook the rice for about 15 - 20 minutes. Drain and set aside. Meanwhile, sautee the onion with a generous amount of olive oil, seasoning with salt and pepper, until translucent, ~8 minutes. Set aside.
Grate the tomato by cutting in half width-wise and grating the flesh against a cheese grater. Put the grated tomato flesh and its juices in a large bowl. To the large bowl, add and combine the chopped dill and mint, cooked onion, garlic, tomato paste, oregano, salt and pepper to season, and the rice.
Preheat the oven to 350F/180C. Then, in a round 10 inch casserole (or rectangular), oil the dish well with olive oil, set aside.
On a large clean surface, lay out your grape leaves a few at a time, and place a generous tablespoon/dessert spoon size of filling depending on the size of the leaf at the bottom tip of the leaf where the stem was. Roll from the bottom, fold in the sides, and roll forward to seal. Kind of like a burrito. Put the dolma with the rolled side where it's 'sealed' down and continue with the rest of the leaves, placing them side by side in the casserole dish. As you place the rolled dolma in the casserole, don't be afraid to pack them somewhat tightly but remember they'll expand a bit as they cook. It's more important though that there aren't any major open spaces when you're done, otherwise the dolma may open during cooking.
Douse the dolmadakia with a good splash of olive oil, be generous! Oil is what makes the difference between sumptuous, flavorful dolmadakia and dry, pathetic ones.
When complete, add enough water to the dish to cover the dolmadakia plus about a generous 1/2 inch. Place an bake-proof plate on top of the dolmadakia that covers them completely leaving about 1 inch at the edges. The idea here is to gently weigh down the dolmadakia so they don't open up while cooking. If you don't have a plate, do the double-foil trick, i.e. gently place a piece of foil on top of the dolmadakia and crush/wrap the edges inwards so it sits inside the casserole and gently presses down on the dolmadakia. Then (for both plate and foil-method) take another piece of foil and wrap to seal the top of the casserole dish. Bake for ~20 minutes and then remove the top foil layer. Bake for another ~15 minutes until the liquid is mostly absorbed.
Let cool slightly. Squeeze the lemon half over the dolmadakia. Serve warm or at room temperature. Great with yogurt.