Choose medium-sized green peppers. Wash them and cut out the stems. Core with an apple-corer or paring knife.
Make the stuffing by lightly frying the pine nuts and chopped onions in 2 Tbsp olive oil. Add the washed rice and cook, stirring, for five minutes.
Add the currants, salt, pepper and sugar. Pour in water to about twice the depth of the other ingredients in the pot and simmer until the water is absorbed. Add mint, allspice and lemon juice.
When cool, stuff each pepper loosely, as the rice will swell. Cover open end of pepper with a slice of tomato like a lid. Set the stuffed peppers in a single layer in a large pan or dish. Sprinkle with salt and sugar, drizzle a little olive oil and 1 cup of water over them and simmer very slowly until the peppers are just tender. Decorate with chopped parsley, lemon slices and tomato slices or wedges, and refrigerate. Serve cool.