Butter a large bowl, and melt 4 tablespoons butter in a saucepan over medium-low heat; let cool. Combine 2 tablespoons melted butter, the flour, water, 1/3 cup honey, the eggs and the egg yolks, yeast and salt in a large bowl. Mix until dough forms. Turn dough out onto a floured surface and knead until smooth, about 10 minutes.
Transfer dough to a buttered bowl, and brush with 1 tablespoon melted butter. Cover with plastic. Let rise in a warm place until dough almost doubles in volume, about 1 1/2 hours.
Turn dough out onto a floured surface. Pat into an 8 1/2-inch x 14-inch rectangle. Top with apples; knead to incorporate. Return to bowl. Brush with remaining tablespoon melted butter; cover. Let rise again in a warm place until dough almost doubles in volume, about 1 hour more.
Preheat oven to 375 degrees F., with a rack in lowest position. Butter a 9-inch round cake pan. Roll dough into a rope (about 24 inches) on a floured surface. Coil into a circle, and transfer to pan. Butter plastic wrap, and cover dough. Let rise again until dough almost doubles in volume, about 45 minutes more.
Heat remaining 4 tablespoons butter and 1/3 cup honey in a saucepan over medium-low heat until butter melts. Brush dough with half the honey-butter. Bake until golden brown and firm, about 35 minutes.
Brush challah with the remaining honey-butter. Let cool in pan on a wire rack for 30 minutes. Turn out loaf from pan, and let cool.