In a 10- to 12-inch heavy skillet (preferably well-seasoned cast-iron for nonstick), sauté the onions in 2 tablespoons oil over medium heat, lifting and turning them occasionally, until soft and golden at the edges, 10 to 15 minutes. Add the artichokes and garlic, if using, and continue lifting and scraping for 5 to 7 minutes, until the artichokes are cooked through and the onions are dotted with dark gold. Generously season with salt and pepper and add the vinegar. Cook for a few minutes over high heat, stirring, until the vinegar is completely evaporated and just a soft, acidic sparkle remains. Taste again for seasoning, then remove from heat and let cool to room temperature.
Break the matzohs into 2- or 3-inch pieces and place in a bowl. Cover with cold water and soak for 5 minutes. Meanwhile, beat the eggs in a large bowl until light and foamy. Drain the matzoh in a colander, pressing out all the water with your hands or the back of a spoon, and add to the eggs. Add the dill and oregano, and season with salt and pepper to taste. Stir in the artichokes and onions and combine thoroughly.
Please read “Making Matzoh Brie” and choose the cooking style you prefer. Wipe out the skillet thoroughly, add the remaining 3 tablespoons olive oil or 2 tablespoons oil and 1 tablespoon butter and heat until sizzling. Add the matzoh batter all at once, and cook either frittata-style (in one piece, waiting until the the entire piece is golden brown before turning, or break it into sections with the spatula to turn it) or scrambled egg-style (lifting and turning pieces as different egg-soaked matzohs begin to set). Or drop it in by heaping tablespoonfuls, like pancakes, and fry over medium heat, until golden brown on the bottom, then turn and fry until done to taste on the other side (either golden and fluffy or more well-done and crisp).
Serve matzoh brie as soon as it is done, accompanied, if desired, by the yogurt cream or yogurt and sprinkled with additional fresh dill or mint.