I got it. A little reading, a little tinkering and this shabbat's result elicited the comment "you got it, Mom!". That's about the highest praise I can receive.
1 kilo (2.2 pounds) flour
2 Tablespoons active dry yeast
1/2 cup sugar
1 tablespoon salt
1 egg yolk
½ cup oil
¼ cup honey
2 cups warm (about 100 degrees) water
Place all ingredients in the bowl of a mixer, with the dough hook attached. Start the mixer on the lowest speed, and once all of the flour has been incorporated, turn it up to medium high speed and let the mixer go for ten minutes.
Put the prepared dough into a large, lightly oiled bowl and cover with a clean dish towel. The dough will be quite sticky. Place in a warm place (the counter near the pot of chicken soup lightly bubbling on the stove is an ideal spot) and let rise until doubled in bulk - about two hours. Lightly press down and let rise again for about an hour. Lightly press down again, then divide the dough into 3 or 4 equal portions, depending on whether you want 3 large or 4 medium challahs. Divide each portion into 3 portions, shape each into a long snake and braid.
Set shaped challahs onto parchment paper lined baking sheets, cover with a clean dish towel and let rise one more hour.
Preheat oven to 350 degrees. Put a large jelly roll pan on the lowest baking rack and fill with boiling water once it's on the rack.
Brush challahs with beaten egg, and, if desired, sprinkle with poppy seeds, sesame seeds or salt.
Bake 30 minutes.