First, you'll need to activate your yeast. Do this by adding the yeast, warm water and sugar into the bowl of your mixer. Leave it to sit for five minutes, or until it becomes foamy.
Next, add the flour, salt, oil, and eggs to the activated yeast. Using the dough hook attachment, mix the dough for five minutes. The dough should take shape and pull away from the sides of the bowl.
Turn out the dough into a large greased bowl and cover it with a clean dry towel. Let it rise for 1 hour, or until it has doubled in size.
Before you start working the dough, preheat the oven to 375 degrees.
After your dough has risen, turn it out onto a lightly floured surface. Divide the dough into three equal sections using a dough scraper or knife.
Take each section of dough and begin rolling them out into long ropes, maybe 12 inches long. I find it is best to start in the center of the dough, rolling my hands down and away from the center.
Finally, once you have three ropes roughly the same size, lay them next to each other on your work surface, lengthwise in front of you. Pinch together the top ends of the dough and then begin braiding the loaf.
Once the loaf is braided, pinch the bottom ends of the dough together and carefully tuck both the top and bottom ends underneath the loaf. Transfer to your parchment lined baking sheet and let rise for 45 minutes.
Once your dough is soft and risen, mix together the egg, cream and water. Using a brush, gently brush on the egg mixture to every visible surface of the dough, then sprinkle with everything bagel seasoning.
Bake in the oven on a middle rack for 28 minutes.