Pile the flour onto the counter. Create a well in the centre of the flour.
Crack the eggs into the well of the flour. Don't worry, the sides of the well will retain the eggs inside. Use a fork to gently beat the eggs.
Using the fork, gradually shift the flour from the walls into the eggs. Continue bringing the flour into the eggs until a dough begins to form.
Knead the dough with your hands and continue adding flour until the dough is no longer sticky. Slice the dough into two equal portions, cover with a clean tea towel and let the it rest while starting the sauce.
Warm olive oil in a large sauce pan, over medium heat. Add garlic and tomatoes to the warmed olive oil. As the tomatoes heat up some of them will pop open and others will wilt. When the tomatoes look nice and wilted toss in the chopped basil.
On a lightly floured surface, roll one portion of the dough into a large rectangle. Roll the dough out until it is thin enough to see your hand through the dough.
With a sharp knife, slice the dough into 3/4" strips. Place pappardelle into a large pot of boiling, salted water and cook for 2-3 minutes.
Remove cooked pasta from water and add directly to the sauce in the sauce pan. Toss with the cherry tomato sauce and serve.