In a bowl, mix together the two types of flour and create a well.
Add in the eggs and yolks. Using a fork, whisk the eggs, slowly bringing in the flour to form the dough.
Once the dough has formed, knead for about 10 minutes.
Wrap tightly in plastic wrap and let rest for a minimum of 30 minutes. The dough can also be made ahead of time and rest overnight.
For the filling, add the burrata to a blender along with the Parmigiano, lemon zest and salt.
Add the filling to a piping bag and set aside.
After the dough has rested, divide into four even pieces and roll out into long, thin sheets.
Using a round fluted cutter, about 3-4 inches in diameter, cut small circles for the cappelletti.
Place about ½ tbsp. of the filling onto each circle and shape the cappelletti.
Bring a large pot of water to a boil, add plenty of salt.
Cook the cappelletti until they float to the top, about 2-3 minutes.
In a large sauté pan over low heat, melt the butter and add the juice of ½ lemon.
When the pasta has finished cooking, strain and add directly to the pan with the lemon butter sauce and toss over low heat.
Plate and top with basil and more Parmigiano.
