Start making the pasta dough. Pour the semolina flour in a bowl and add a little bit of water at a time while mixing with your hands; when it starts to come together, add the olive oil and salt. Knead the dough for 8-10 minutes adding more water if it crumbles or more flour if it's sticky until it becomes a smooth elastic ball.
Cover the pasta dough in plastic wrap and set aside to rest.
Make the Sauce
In a medium pan or pot, drizzle some olive oil and add the mashed garlic cloves. Turn on the heat to low and when the garlic starts to sizzle, add the canned tomatoes.
Mix with a wooden spoon and turn the heat to medium. Add a teaspoon of sugar to break the acidity of the tomatoes (add more if needed), then add the chili pepper flakes and salt to taste.
Bring to simmer than turn the heat again to low and let it simmer for about 15-20 minutes.
Roll the Pici
While the sauce simmers you can roll out the pici. Dust a cutting board (better wood or marble) with semolina flour and knead the pasta until it doesn't stick anymore to the cutting boeard, then roll it with a rollin pin until it's about ½ cm (¼ inch) thick then cut it into stripes of the same thickness.
Roll the stripes of dough between your palms or on the cutting board as you prefer until you have Pici (you may cut the stripes in half if they are too long, Pici should be more or less as long as Spaghetti).
Boil the pici in salted water for about 10 minutes or until al dente.
Drain the pasta and toss is the sauce; remove from heat and serve with grated Pecorino or Parmesan cheese on top.
Notes
You can store leftovers in an airtight container in the refrigerator for 3-4 days. Reheat in the microwave or on the stove with a splash of water until warm through.