Bring all wet ingredients to room temperature (including eggs). Mix eggs, molasses, oil and cider vinegar in a large mixing bowl. Combine dry ingredients, including yeast, in a separate bowl and whisk well.
Slowly stir the dry ingredients into the wet, adding the water and apple cider last to help keep flour dust in the bowl while mixing. Continue to mix on medium speed until all lumps are smooth, approximately 2-3 minutes. The batter will be very wet like a cake batter, not like a typical bread dough.
Meanwhile prepare one 9×5 inch bread pan and three mini loaf pans, or two 9×5 inch bread pans or one 12×4 1/2 inch Pullman bread pan by oiling well or lining with parchment.
Pour batter into pans, but do not fill more than 2/3 full. Cover with oiled parchment paper and allow to rise for 45 minutes in a warm place like an oven set to 200°F then turned off. Watch to be sure the loaves do not rise above the top of the pans.
Preheat oven to 350°F (static) or 325°F (convection) and bake mini loaves for 15-20 minutes, larger loaves for 35-40 minutes, removing only when internal temperature is at least 205°F and a toothpick or skewer inserted into the center of each loaf comes out clean.
Allow to cool for 5-10 minutes in the pan before removing to finish cooling on a wire rack. Slice once cooled. Keep fully cooled loaves in a zip-top bag at room temperature.
Bread machine method (3lb loaf):This recipe makes a large loaf, so set your bread machine to its largest loaf setting (3lbs if that's an option). Because of the size of the loaf, a typical bread machine cycle may not bake it all the way through. Be prepared to add time at the end of the bake cycle, either on the machine if it will allow it, or by preheating your oven to 350° F and moving the bread pan to the preheated oven to add bake time.
The bread may sink in the middle somewhat (I've made several of these breads in various breadmakers, and they sometimes look a little funny on the top edge (a little like bat's ears - my kids love it, actually!), but the crumb is still gorgeous and the loaf should still cook all the way through, once it's reached an internal temperature of 205 - 210° F).
Bring all wet ingredients to room temperature, whisk together, then pour into the bread pan. Whisk together dry ingredients (except for yeast) in a separate bowl, then pour on top of the wet ingredients in the pan. Make a well in the center with your finger, then pour in yeast.
Set bread maker to gluten-free bread setting, OR, if your machine does not have a gluten-free setting, use “Dough” setting or a setting for mixing and rising only. Do not let the machine “punch-down” the bread or set for second rise. After rising, set machine to “Bake” for 60 minutes.
Remove only when the bread has come to an internal temperature of 205-210°F. If necessary, add bake time to the bread machine or when finished the bread machine cycle, finish baking in an oven preheated to 350°F.
Leave bread in the pan for 5-10 minutes before inverting gently to remove. Finish cooling on a wire rack and slice when cooled. Keep fully cooled loaves in a zip-top bag at room temperature.