Heat a large skillet to medium-high heat and add 1-2 tbsp of avocado oil to the skillet. Season the chicken breasts with Italian seasoning, salt and pepper.
Add the chicken the hot skillet, making sure not to over crowd the skillet, and cook through, about 4-5 minutes per side.
Transfer cooked chicken to a plate and top each piece with a slice of mozzarella. Quickly cover the plate with foil and set aside, allowing the cheese to melt.
Lower heat to medium-low. If desired, splash wine into the pan and deglaze browned bits with a wooden spoon (we did not use wine in the video). Allow the wine to reduce slightly, about 1 minute, then stir in butter and add halved tomatoes.
Allow the tomatoes to blister, about 3-5 minutes.
Turn the heat off and stir in the lemon juice and half of the fresh basil.
Add the cheesy chicken back into the hot skillet, top with blistered tomatoes, drizzle with a little olive oil and top with remaining fresh basil prior to serving.