Step 1 To mix in a heavy-duty mixer with a dough hook: Place the flour and eggs in the bowl of an electric mixer with a dough hook. Start mixing and add oil and salt. When incorporated, add 1 teaspoon water slowly. Only add enough to get the dough to clump up; too much will make the dough too wet and sticky. With the dough hook, knead for about 10 minutes. Pull the dough together, wrap it in plastic wrap and let rest 30 minutes. Go to step 3.
Step 2 To mix by hand: Mound the flour on the center of a wooden board. Make a well in the center of the flour. Drop the eggs, oil and salt into the well. With a fork, mix the eggs and oil and slowly incorporate flour into the egg mixture from the inner well wall. Keep incorporating flour into the mixture bit by bit. As you expand the well, make sure you keep moving flour upward from the base in order to maintain the well shape. It will start to come together when half the flour is incorporated. Knead the dough with the palms of your hands until it forms a cohesive mass. Lift the dough from the board and scrape away any stray bits of dough. Lightly re-flour the board and knead for 6 to 8 more minutes. Dough should get elastic and slightly sticky. Wrap it in plastic wrap and let it rest 30 minutes. Go to step 4.
Step 3To roll out the dough: Cut off a small piece of the dough and flatten it a bit with your hand. Lightly dust with semolina flour. Set the pasta machine to the thickest setting and push the dough through a few times until it is shiny and elastic. Re-dust with a bit more semolina. Adjust the roller to next thinnest setting and run the dough through again, trying to maintain an even, rectangular shape. Repeat the dusting and make the roller setting thinner until you have a translucent sheet of dough (setting No. 6 on the Kitchen Aid pasta-roller attachment or a hand-cranked machine is perfect).
Step 4Cut the dough into 2 1/2 -inch squares with a pizza cutter. With a brush, very lightly apply the egg wash to the dough.
Step 5Place a scant teaspoonful of filling on the center of the square and fold into a triangle. Try to squeeze as much air out of the center as you seal the edges with your fingers. Place on a cookie sheet lined with parchment or wax paper dusted with semolina. (Kreplach may be frozen at this point. When they are frozen remove from pan and place in freezer bags until ready to cook. They may be cooked from frozen. If you do not freeze them, they must be cooked within 4 hours or they may get too soft and burst while cooking.)
Step 6Cook the kreplach in salted boiling water, about 5 minutes for frozen, 4 minutes for fresh.
Step 7To serve, ladle hot chicken broth into a warmed soup bowl. Add about 5 cooked kreplach. Garnish with chopped parsley and dill.