Step 1Saute onions in 2 tablespoons oil in 10- to 12-inch heavy cast-iron or nonstick skillet over medium heat, lifting and turning them occasionally, until soft and golden at edges, 10 to 15 minutes. Add artichokes and garlic, if using, and continue lifting and scraping 5 to 7 minutes, or until artichokes are cooked through and onions are dotted with dark gold. Generously season with salt and pepper and add vinegar. Cook a few minutes over high heat, stirring, until 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.
Step 2Break matzos into 2- or 3-inch pieces and place in bowl. Cover with cold water and soak 5 minutes. Meanwhile, beat eggs in large bowl until light and foamy. Drain matzo in colander, pressing out water with your hands or back of a spoon, and add to eggs. Add dill and oregano and season with salt and pepper to taste. Stir in artichokes and onions and combine thoroughly.
Step 3Wipe out skillet thoroughly, and heat remaining 3 tablespoons oil over medium-high heat until sizzling. Add matzo batter all at once, and cook either frittata-style (in 1 piece, waiting until whole is golden brown before turning, 4 to 5 minutes per side side, or break it into sections with the spatula in order to turn it) or scrambled egg-style (lifting and turning pieces as different egg-soaked matzos begin to set), 6 to 8 minutes total. Or drop it in by heaping tablespoonfuls, like pancakes, and fry over medium heat until golden brown on bottom, then turn and fry until done to taste on the other side, (either golden and fluffy or more well-done and crisp), about 3 to 4 minutes per side.
Step 4Serve immediately with yogurt mixed with chopped onions and garnished with additional dill, if desired.