Build the sandwich in this order: bread, mozzarella, tomato, big pinch of salt, basil, bread.
Crack the egg in a wide, shallow bowl or rimmed plate (or even a pie pan) and beat with a fork until smooth.
Set a preferably nonstick skillet over medium heat and add the olive oil. While that gets hot, carefully dip both sides of the sandwich in the egg. It will soak up most of the egg but not all.
When the oil is shimmery, add the sandwich. It should sizzle. Cover the pan with a lid. (If this slightly squashes the sandwich, good! But no need to press down—that will come later.) Cook for about 3 minutes until the bottom is deeply browned. Remove the lid and use a spatula to flip. Use the spatula to press down on the sandwich—firmly to condense but not so harshly that the fillings squish out. Cook for another 2 or so minutes until the bottom is deeply browned.
Remove to a plate, let cool for a moment, then slice in half on the diagonal.
Emma is the food editor at Food52. Before this, she worked a lot of odd jobs, all at the same time. Think: stir-frying noodles "on the fly," baking dozens of pastries at 3 a.m., reviewing restaurants, and writing articles about everything from how to use leftover mashed potatoes to the history of pies in North Carolina. Now she lives in Maplewood, New Jersey with her husband and their cat, Butter. Stay tuned every Tuesday for Emma's cooking column, Big Little Recipes, all about big flavor and little ingredient lists. And see what she's up to on Instagram at @emmalaperruque.