Place the warm water and non-dairy milk, sugar, oil and yeast in a bowl. If using instant yeast you can proceed directly with the next step. If using active dry yeast, wait a few minutes to make sure the yeast blooms.
Add 3 cups flour to the bowl along with salt. Knead in a stand mixer or by hand until a smooth dough forms. Add more flour as necessary if the dough is too sticky. Once the dough comes together, continue kneading on medium-low speed for eight more minutes, or by hand.
Form the kneaded dough into a smooth ball. Place in an oiled bowl, turning the dough over once to coat the top with oil. Cover the bowl and set it in a warm spot.
After 1 to 1 ½ hours the dough should have doubled. Remove it from the bowl and punch it down.
Divide the dough in half and shape each half in a ball. Roll out one ball of dough into a disc, 10 inches in diameter. Use a pizza cutter or knife to cut into eight wedges, like you'd cut a pizza.
(See pictures above for clarity on this step) Take one wedge and pull the sides with your fingers to lengthen them. Pull the bottom point to a pointed shape. Begin rolling the edge toward the point to form a crescent shape. Tuck the pointed end under the roll and curve the sides toward you to form a crescent.
Repeat for remaining dough until you have 16 rolls. Place the rolls on a lightly oiled baking sheet, cover loosely with a towel and let them rice another hour or until they have doubled in size.
About 15 minutes before the rolls have finished rising, preheat the oven to 425 degrees Fahrenheit/220 degrees Celsius.
If using the optional "egg" wash, mix the milk, sugar and oil. Brush it on the risen rolls.
Bake the crescent rolls for 15-18 minutes. The rolls should be golden-brown on top when done. Cool on a rack. You can serve the rolls warm or at room temperature.