Burekas with Egg is not a different pastry but a way of serving one: a baked burekas split open and built into a fuller plate with a hard-boiled egg and pickles, the standard street treatment at burekas stands across Israel. The angle is assembly rather than baking. The pastry has already done its work; the question is how the additions turn a single hand-held item into something that eats like a meal without drowning the leaves it took skill to make crisp. Done right it is a balanced little composition; done wrong it is a soggy bag of good pastry weighed down by everything piled on it.
The build starts with the burekas itself, most often the cheese or potato version, fresh and warm from the case. It is slit along one edge and the additions are tucked inside or stacked alongside on the paper. The defining element is a hard-boiled egg, usually a soft-set yolk, halved or quartered and pressed lightly into the opening, often with a dusting of salt. Pickled cucumbers come next for acid and crunch against the rich pastry, and the finish is a spoonful of tomato relish, a chunky cooked tomato and onion sauce, or s'chug for heat, sometimes both. Some stands add a little chopped Israeli salad or a smear of tahini. Done well, the egg is just set and creamy, the pickle is sharp, the relish is bright and not watery, and the pastry stays crisp because the wet elements sit beside it rather than soaking into it. Done badly, the egg is grey and chalky, the relish is thin and floods the leaves, or so much is added that the burekas folds shut and the whole thing has to be eaten with a fork it was never meant to need.
Within this serving the variation is in the additions and the base pastry. The egg can be quartered cold or mashed loosely with the relish into something closer to a spread, and the heat ranges from a token spoon of mild tomato sauce to an aggressive load of s'chug. Tahini, amba, or a handful of olives show up regionally. The choice of underlying burekas changes the plate entirely: the salty cheese version against bright relish reads differently from the mild potato version doing the same job. The individual fillings, meat, cheese, mushroom, potato, and spinach, are each documented in their own articles as pastries in their own right; this one is specifically about the assembled plate they all pass through. On its own terms, burekas with egg is a discipline of restraint at the counter: enough to make a meal, never so much that the pastry stops being the point.