Slice chicken breasts into 8 thinner cutlets lengthwise. I cut them on a diagonal starting at the thickest part, making it thinner. Pound with a rolling pin or flat side of a meat mallet into same thickness pieces. Season with 1/2 teaspoon salt and 1/2 teaspoon black pepper on both sides. Set aside.
Preheat large skillet on medium heat and swirl 1 tablespoon of olive oil to coat. Pan fry chicken until golden brown or for about 6 minutes per side. Transfer onto a plate and set aside.
Return skillet to medium heat and add remaining 1 tablespoon of olive oil. Add onion and cook until softened, stirring occasionally. Add garlic and saute for another 30 seconds, stirring a few more times.
Add flour and stir until combined. Now start adding chicken broth in small increments while stirring, until thick roux forms. Then add milk, heavy cream, remaining 1/2 teaspoon salt, 1/4 teaspoon pepper, stir and bring to a boil. Add lemon juice and give sauce quick mix.
Add previously cooked chicken, making sure to cover it in sauce, and simmer on low heat for 5 minutes or until sauce has thickened a bit and chicken is tender. Sauce will thicken more as it stands. Tuck in lemon slices.
Let lemon garlic chicken stand for 3-4 minutes, garnish with parsley and serve with your choice of pasta, grain or salad.
Notes
Store: Refrigerate any leftovers in an airtight container for up to 3 days.Freeze: Freeze cooked and cooled chicken in airtight container for up to 3 months. Thaw in the fridge overnight before reheating.