Step 1

Make the curd: Whisk together sugar and yolks in a 2-qt. saucepan; add butter, zest, and juice, and whisk until smooth. Place over medium heat, and cook, stirring, until curd is the consistency of loose pudding, 8 to 10 minutes. Pour curd through a strainer into a bowl, and press a piece of plastic wrap on the surface of the curd; chill for 2 hours.

Step 2

To make each sandwich, heat a 10" nonstick skillet over medium-high heat. Brush one side each of 2 slices brioche with butter, and place in skillet, buttered sides down, and toast, about 1 minute. Transfer slices to a plate, toasted sides down, and spread 1⁄2 oz. goat cheese over one slice and 2 1⁄2 tbsp. lemon curd over the other slice.

Step 3

Meanwhile, whisk 1 egg in a bowl, and add to skillet; sprinkle with 1⁄4 tsp. thyme and salt and pepper, and cook, flipping once, until just set, about 2 minutes. Fold up omelet and place on top of the goat cheese. Place 4 slices ham in skillet, and cook, flipping once, until heated through, about 35 seconds; place on top of omelette. Place 1 oz. mâche on top of ham, then top with the bread slice slathered with lemon curd. Repeat with remaining ingredients to make 3 more sandwiches.