Place the flour on a clean work surface and make a well in the middle of the flour. Add the oil, water and salt and incorporate with a fork until you can work it with your hands. Knead the dough, using the heel of your hand to push down onto the flat surface and rotating the dough as you knead. Repeat this until the dough is smooth and bounces back when you press it with your finger. This process takes about 10 minutes.
Make a disc with the dough about 2 inches thick and wrap it in plastic wrap. Let it rest for at least 15 minutes or up to 3 hours at room temperature.
To shape cavatelli, divide the dough into eight pieces (thin slices of the disc work best here). Roll each piece into a thin rope about ¼” (6mm) thick one at a time. Leave the remaining dough wrapped until you finish cutting and shaping each rope. Using a bench scraper or knife, cut the rope into small pieces, between ½” and 1” depending on how large you want the pasta to be.
Next, depending on the size of your fingers, press each piece down with 1-3 fingers and drag it toward you to create an indentation in the segment. The edges will curl slightly to give you the cavatelli shape. You could also use a gnocchi board if you want grooves on your cavatelli. Once made, they can be used immediately.
Bring a large pot of water to a boil, salt the water so it tastes like the sea (about 2 tablespoon of salt for every 6-8 quarts of water). Add the cavatelli and cook for 4-5 minutes. Taste after 4 minutes and if they aren't quite done, taste again 1 minute later. Fresh cavatelli pasta (cooked the same day) should take 4-5 minutes (add more time for dried cavatelli or frozen cavatelli). Drain in a colander and use with any sauce you choose. Buon appetito!