Heat the mozzarella and butter together in a saucepan over medium heat, stirring as they melt. Look for a soft, stretchy cheese mixture without firm pieces.

Work the almond flour into the melted mixture until it gathers together. The loose flour should disappear into a cohesive, dough-like mass.

Whisk the whole egg and extra yolk in a separate bowl, then knead them into the cheese mixture once it is comfortable to handle. The finished dough should look evenly combined, without visible streaks of egg.

Shape the dough into an even rope about ½ inch thick. A consistent thickness helps the pieces cook at a similar pace.

Divide the rope into 1-inch pieces with a knife. Aim for evenly sized dumplings rather than perfectly identical shapes.

Give the shaped dumplings 5 to 10 minutes in the freezer. They should feel firmer and less prone to losing their shape.

Fill a large sauce pot with water and bring it to a boil. Wait for steady bubbling before adding the dumplings.

Lower one-quarter of the gnocchi into the water, reserving the rest for subsequent batches. The uncrowded pot helps the water maintain its heat and the pieces remain intact.

Watch the batch closely and lift out the dumplings when they soften and start rising to the surface. Floating is the cue to remove them rather than leave them boiling longer.

Transfer each cooked batch onto paper towels to drain. The towels should absorb the surface water before the dumplings reach the skillet.

Warm the olive oil in a skillet over medium-low heat, then add the drained gnocchi. A gentle sizzle should begin where the dumplings touch the pan.

Brown the undersides, then turn the dumplings to sear the opposite sides. Remove them when both faces have a golden crust.