Scald milk; remove from heat. Stir in butter, sugar and salt, stirring until butter melts. Pour into large mixer bowl; cool to lukewarm. Place 1/4 cup warm water in small bowl; sprinkle with yeast. Let stand until softened, about 3 minutes.
Add yeast mixture and 1 3/4 cups of the flour to milk mixture. Mix until blended; beat on medium speed until dough is elastic and pulls away from bowl, about 5 minutes.
Beat in eggs, one at a time, beating well after each addition. Beat in 1 cup of the flour. Stir in 1/2 cup of the flour to make soft dough. Turn dough onto floured surface. Knead, adding flour as needed, until dough is smooth and satiny and small bubbles form just under surface, about 15 minutes.
Place dough in greased bowl; turn greased side up. Let stand covered in warm place until doubled, about 1 1/2 hours.
Soak bottom of a 3 1/4 quart (3.25 L) unglazed clay cooker in water about 15 minutes.
When dough has doubled, drain bottom; pat dry; grease sides and bottom generously. Line cooker with parchment paper cut to fit bottom only; grease parchment paper.
Punch down dough. Turn onto floured surface. Knead lightly just to expel air bubbles. Divide into 3 pieces. Roll each piece between palms of hands into 12 inch rope. Place ropes, side by side, in cooker; braid ropes and tuck ends under. Let stand, covered with waxed paper, in warm place until nearly doubled, about 45 minutes to 1 hour. Mix egg white and 1 teaspoon water. Brush dough with egg white mixture; sprinkle with sesame seeds.
Soak top of cooker in water about 15 minutes; drain. Place covered cooker in COLD oven. Set oven at 425°F (This temperature of 425°F is correct the bread will not burn, it is golden brown all over and crusty.) Bake until bread sounds hollow when tapped and crust is brown, 40 to 45 minutes. Remove from cooker; cool on wire rack.