Sure thing. I use a variation of a recipe from Cooks.com. I don't add the extra yolks (I use water) and I mix it all in a big bowl instead of on the counter. Makes cleanup easier, and I can just put the lid on the bowl for the resting period.
Egg Noodles
3 1/2 cups flour
4 eggs, at room temperature
3 egg yolks or 3 T water
1 tsp salt (optional)
Measure flour and pile in a mountain shape on a clean board. Scoop a well in the center and pour eggs into the well. Add salt.
Using your fingertips, stir tiny portions of flour from the inner edges of the flour mound into the egg, incorporating just a little at a time. Keep stirring until all of the egg/water and flour is combined to make a pasty mass of somewhat sticky, but dryish dough.
Gather the dough into a mound, make a new indent at the top and then add yolks (or water). Knead the dough into a smooth ball, adding tiny amounts of flour as needed, but try to avoid adding too much. Roll into a ball, cover with an inverted bowl or plastic wrap and let it rest for 20 - 30 minutes. (This is important so don't skip this step.)
Dust your work surface and rolling pin with flour. Roll the dough flat, fold into thirds over itself and roll out again, stretching the dough until it is flat and smooth. If you're going to cut them by hand, do this several times. Then roll it up like a big jelly roll and slice your noodes.
I use a pasta machine, so I cut off balls of dough and run them through the rollers several times, then lower the setting. On my machine, #3 makes a thick noodle, similar to what purchased frozen noodles are. I roll out a long strip, then cut it to the length that I want the noodles to be. Run it through the machine, dust with flour and toss them on a cookie drying rack, towel, whatever to dry. Around here, everything has to be covered, so I put a thin dishtowel (or paper towel would work) over the noodles.
I keep checking my noodles, tossing them with flour again if necessary. One time I ended up with a big glob and had to cut them all again! After they're dry enough so they don't stick to each other (takes hours here) I freeze them in meal size portions in freezer bags.
Some times I use three eggs and more water. They still turn out good. I have also used refrigerated eggs and didn't notice much of a difference in rolling.
If you use farm eggs, the noodles will be fairly yellow. If you want colored noodles, sub vegetable puree for the water: Spinach for green, carrot for orange, beet for red. I have never done it, but read that the dough will be mottled at first, but become smoother with successive rollings.