How to Make It
Combine water and yeast in the bowl of stand mixer fitted with the dough hook and mix to combine. Let sit until foamy, about 5 minutes. Meanwhile, whisk 5 cups flour and salt in a large bowl.
With the mixer on low, slowly add flour mixture until well combined, 2 to 3 minutes (dough will be shaggy). Add 2 tablespoons oil and continue to mix until oil is absorbed, about 1 minute. Increase speed to medium-low and knead until dough is soft and pulls away from sides of bowl, about 5 minutes. If dough is very sticky, add remaining ½ cup flour, one tablespoon at a time until dough is smooth. Transfer dough to counter and shape into a ball. Wipe out the mixing bowl, grease with 2 teaspoons oil and add dough, turning to coat in the oil. Cover bowl with plastic wrap or a tea towel and let rise in a warm, draft-free place until doubled in size, about 1½ hours.
Preheat oven to 425°F. Grease a standard 13-by-18-inch baking sheet with 1 tablespoon oil. Punch down on dough, remove from bowl, and transfer to greased tray. Using your fingertips, press dough to the edges of the tray. Cover with plastic wrap or a tea towel and let rest again until slightly risen, about 1 hour. Press all over the dough with your fingertips to create dimples in the dough.
Just before baking, combine ¼ cup boiling water and baking soda (mixture will bubble); brush on dough to cover the surface. Discard remaining baking soda mixture. Brush top of dough with egg and top with ¾ teaspoon flaky salt. Bake until golden, 18 to 20 minutes.
Brush focaccia with remaining 1 tablespoon oil and top with remaining ¾ teaspoon flaky salt. Let cool slightly while you make the cheese sauce.
For the cheese sauce: mix cheese and cornstarch in a bowl. Combine half and half, cream cheese, and mustard in a small saucepan and cook over medium, stirring frequently, until combined, about 2 minutes. Slowly add cheese mixture, stirring throughout, until cheese is melted and sauce is thick, about 3 minutes. Stir in parsley. Cut focaccia into 22 strips. Serve with warm cheese sauce.