Step 1
Combine milk flour and eggs in a blender. Blend until smooth about 1 minute.
Step 2
Heat a nonstick pan over medium-high heat. Brush hot pan with a small amount of butter. Ladle about 3 tablespoons of batter into the center of the pan. Tilt pan from left to right to cover entire surface. Sprinkle top of the crepe with 1 or 2 teaspoons of basil.
Step 3
Cook until edges begin to brown 2 to 3 minutes. Flip crepe over and cook until set about 2 minutes more. Remove to a plate. Cook remaining batter re-brushing pan with butter and stacking crepes with parchment paper in between.
Step 4
Mix chicken grapeseed oil balsamic vinegar and salt together in a resealable zip-top bag; marinate for 20 to 30 minutes.
Step 5
Drain and discard marinade. Heat a skillet over medium-high heat. Add chicken; cook and stir until juices run clear about 5 minutes.
Step 6
Place broccoli in a microwave-safe bowl with 2 tablespoons water. Microwave until crisp-tender 3 to 4 minutes.
Step 7
Combine butter and garlic in the same skillet over medium heat. Cook until fragrant about 1 minute. Add the broccoli; stir to coat with the garlic butter. Stir in tomatoes and mushrooms and heat through.
Step 8
Stir cream cheese and pesto together in a separate saucepan over medium heat. Cook and stir until sauce comes together 3 to 5 minutes.
Step 9
Lay a crepe on a plate line chicken filling down the middle and drizzle sauce on top. Fold crepe over burrito-style; spoon more chicken and sauce over top. Repeat with remaining crepes filling and sauce.