Being very careful, pat burrata with a cloth or paper towel, to dry off extra moisture.
Set up 3 bowls, one with flour, another with the whisked egg, and then the last one with the mixed panko and seasonings.
Roll the burrata into the flour, then egg, and then panko mixture. Then repeat with the egg and panko mix again. Place on a parchment lined baking sheet or freezer safe container. Repeat with the second burrata ball.
Place the breaded burrata in the freezer for around 45 minutes. (This step is important to help prevent leaking, or bursting, while cooking)
Towards the end of the freezer time, add enough canola oil to a small deep pot to cover the bottom of pot 2 inches. Heat the oil on medium until about 350F (or oil is ready when the end of a wooden spoon bubbles when pressed to the bottom of the pot).
Once oil is ready, gently place one burrata at a time to the oil and fry about 2 minutes on one side, or until nicely browned, and then carefully and gently flip to fry the other side another 1-2 minutes. (Adjust the temperature according to how fast it is browning)
Remove from oil , place on paper towel lined plate, and sprinkle with flaky sea salt. Repeat with second burrata.
Once burrata is fried. Make the Creamy Pesto Sauce.
In a small skillet over low-medium heat, add the butter and flour. Stir together to make a rue until it gets a little bubbly and thick.
Then add in the pesto and stir until combined well. Slowly drizzle in the milk while stirring until everything is combined well and not lumpy. Bring to a simmer. Then adding the salt and fresh parmesan cheese and stir until combined well.
Spoon the creamy pesto onto a plate. Place a burrata ball on top, sprinkle a little parmesan cheese on top and a drizzle of balsamic glaze.