Pat the burrata dry using paper towels so coating sticks properly. Prepare three bowls containing flour, whisked eggs, and breadcrumb mixture. Season each layer lightly to build flavor.
Coat burrata gently in flour, dip into egg, then roll in breadcrumb mixture. Repeat egg and breadcrumb coating if you want extra crunch. Chill coated cheese briefly so coating firms up.
Heat oil to medium-high temperature and carefully add coated burrata. Fry until golden and crisp, about 2–3 minutes per side. Remove and drain on paper towels.
Heat olive oil in saucepan and sauté garlic until fragrant. Stir in tomato paste and cook until slightly darkened. Slowly whisk in cream until smooth.
Add red pepper flakes, basil, salt, and pepper to sauce. Simmer until thickened, then stir in butter and Parmesan for richness. Keep sauce warm for serving.
Spread warm sauce on a serving plate and place fried burrata on top. Garnish with fresh basil and serve with toasted bread. Cut open burrata and enjoy the creamy center.