Combine marinade ingredients in a gallon size Ziploc bag. Squish around the chicken and marinade so that all the chicken is fully coated. Refrigerate for a minimum of 30 minutes.
After chicken has marinated, pre-heat grill on high heat for 15 minutes. Remove chicken from marinade and discard bag. Place chicken on grill and cook on each side for 10-12 minutes or until chicken is cooked to an internal temperature of 165°F. Adjust grill heat while cooking to ensure that there is a little bit of char, but the meat does not burn or catch on fire.
While chicken is grilling, prepare the lemon butter sauce. Heat butter in a skillet over medium heat. Add the garlic paste, basil, and tomato oil to the butter and saute for 1-2 minutes.
Squeeze lemon juice into the butter mixture and whisk to combine. Reduce heat to low. Slowly drizzle heavy cream into the skillet while whisking. Continue cooking on low for 2-3 minutes until sauce is well emulsified and thickened slightly. Remove from heat.
Plate one piece of grilled chicken. Spoon several tablespoons of sauce over the chicken. Top with a spoonful of sundried tomatoes and 1 oz. of goat cheese. Serve with additional sauce.
