Step 1

Put the potato quarters into a large saucepan with cold water and enough salt to make the water taste like the ocean. Bring to a boil, then cook over medium-high heat until a knife inserted into the potato slips out easily, about 20 minutes. Drain the potato and set aside. When the potato has cooled enough for you to work with it, press it through a fine-mesh sieve, using the back of a ramekin or a large wooden spoon. (If you own a ricer, use it here.)

Step 2

Combine the yeast and sugar in a large wide-mouthed bowl. Add the warm water. (Run the water over the inside of your wrist. When it feels like the temperature of your skin, the water is ready.) Stir together gently. Give the yeast 10 to 15 minutes to proof.

Step 3

Sift the tapioca flour, sorghum flour, potato starch, and sweet rice flour through a fine-mesh sieve into the bowl of a stand mixer. Stir in the xanthan gum, guar gum, and salt.

Step 4

Add the egg yolk, oil, yeasty water, and rosemary to the dry ingredients. Run the stand mixer with a paddle attachment on medium speed until the dough comes together, about 5 minutes. When you first stop the mixer, the dough will look like a firm ball, and then it will start to slump off the paddle attachment. The dough will have the consistency of thick cake batter.

Step 5

Beat the egg white until it is stiff. Gently fold it into the dough. Set the bowl in a warm place and allow the dough to rise until it has doubled in size, about 1 hour.

Step 6

Preheat the oven to 450°F. Grease both sides of a piece of parchment paper with oil and lay it down in a 9-inch pie pan.

Step 7

Push the dough into the prepared pan and smooth the top with a rubber spatula. Sprinkle on olive oil and sea salt, if you wish. Slide the focaccia into the oven and put a large oven-safe saute pan filled with ice cubes on the rack beneath it. Bake until the top is browned and the internal temperature of the bread reaches at least 180°F, about 25 minutes.

Step 8

Allow the focaccia to cool in the pan for at least 10 minutes. Tip it onto a wire rack and cool for another 30 minutes. Enjoy.