In very small skillet, bring 3 tb. sugar to boil, stirring it over moerate heat. Should melt to rich, dark brown. CAREFULLY add the boiling water and stir to dissolve the caramel. Pour into dish to cool. Combine warm water, yeast and remaining tsp. sugar and let stand til foamy. Abt. 10 min. In lge mixing bowl, combine salt, shortening (butter), cooled milk, and liquid caramel. Add yeast mixture. Stir in the pumpernickel and rye flours, then 2 cups of the A/P flour. Spread 1 cup of the remaining A/P flour on work surface and turn the dough out onto it. Gradually incorporate the flour, kneading in as much more as necessary to make a fairly stiff dough. Knead well until the dough is no longer sticky. Form dough into ball and place in greased bowl, turning once or twice. Cover with plastic and place in not too warm place. Let proof until double. Punch dough down, halve it, and roll it into 2 10 inch cylinders. Cover with towel and let rest for 10 min. Cut each cylinder into 10 pcs. Cover with dry towel, then damp one, and let rest another 10 min. Roll each pc. into "snake" abt. 20 cm long, tapered at ends. Wet both ends, overlap abt. 3 cm, and gently pinch ends together. Place finished bagels on 2 baking sheets covered with parchment, cover with towel and let proof until not quite doubled. When ready, brush tops with egg wash and place in 220ºC . oven on 2 racks centered in oven. Bake 10 min. Switch pans and bake 5 to 10 min. more until well browned. Cool on racks. Store in plastic bags up to 2 days. Longer--freeze.