Place pepper directly on the trivet of a gas-stove burner over high heat. As each section turns puffy and black, turn pepper with tongs. (If you don't have a gas stove, place pepper on a baking pan, and broil, turning as each side chars.) Transfer pepper to a small bowl; cover with plastic wrap. Let sweat until it is cool enough to handle, about 15 minutes. Transfer to a work surface. Peel off and discard blackened skin. Cut pepper into 1/4-inch dice, discarding seeds and inner membranes; transfer to a bowl; set aside.
Heat 1 teaspoon olive oil in a skillet set over medium heat. Add onion, oregano, and salt; cook until onion is beginning to brown, about 4 minutes. Transfer to bowl with red pepper. Add cooked brown rice, currants, parsley, zest, and all but 1 tablespoon lemon juice; stir to combine.
Remove stem from a rinsed vine leaf; lay leaf on work surface. Place 1 tablespoon filling at stem end; roll leaf tightly, tucking in ends. Repeat until all filling is used.
Line an 8-inch saucepan with remaining leaves; arrange stuffed leaves, seam side down, in pan. They may be stacked in 2 layers. Drizzle with remaining tablespoon olive oil and remaining tablespoon lemon juice. Add enough water to the pan to just cover stuffed leaves; weight leaves for cooking with a kitchen plate or a lid smaller than the diameter of the pan.
Place saucepan over high heat; bring to a boil. Reduce heat to medium low; allow to simmer gently until leaves are tender, about 45 minutes. Transfer stuffed leaves to a serving platter, and allow to cool. Serve chilled or at room temperature.