In a medium bowl whisk together the eggs and half and half until frothy. Add the tarragon, some salt and pepper, and whisk together. Add the cubed challah and let it soak in the egg mixture for about 5 minutes.
Meanwhile, melt 2 tablespoons butter in a small oven-proof skillet over medium-high heat. Add the ham, peppers and spring onions. Cook, stirring occasionally, until the ham is a bit browned, about 5 minutes. Stir in the remaining butter and spread the ham and vegetables out evenly in the pan. Pour in the challah-egg mixture and let cook for 2 to 3 minutes. Turn the heat to medium-low, cover, and cook until the frittata becomes light and fluffy, about 3 more minutes. Place the pan under the broiler until the top is browned, about 1 minute. Transfer the frittata to a plate and cut into wedges.
Note: If you don't have a broiler, use a heat proof rubber spatula and carefully flip the frittata over, and cook for 1 minute. Or, melt a tablespoon of butter in a separate skillet until it sizzles. Pour the melted butter over the frittata and place the empty skillet over the frittata pan. Holding both handles, carefully flip the pans over, and cook the frittata on the other side for a minute.