Step 1Run each sheet of matzo under cold water for 10 seconds, then set aside on a plate to soften.
Step 2In a large skillet over medium heat, heat oil. Add onions and thyme and season with salt and pepper. Cook, stirring occasionally, until onions are tender and lightly golden, 15 to 20 minutes.
Step 3Add butter to pan, then tear matzo into bite-sized pieces directly into pan. Stir matzo into onions and let toast 2 minutes, then reduce heat to medium-low and stir in eggs.
Step 4Cook, stirring frequently, until eggs are cooked through and fluffy, about 1 minute. Transfer to a plate, season with salt and pepper to taste, and top with chives. Serve with sour cream on the side.