Whisk together flour and Italian seasoning on a plate. Slice the chicken breasts in half, preferably as equal as possible, then lightly coat in seasoned flour. Add 2 tablespoons (28g) butter to a skillet over medium-high heat and once it is hot, add the chicken to the skillet. Brown on both sides, cooking about 2-3 minutes each side. Remove and set on a plate.
Reduce the heat to medium and add the remaining 1 tablespoon (14g) butter to the same skillet then add garlic and cook until fragrant. Add lemon juice, lemon zest, chicken broth, and heavy cream. Scrape the bottom of the skillet to pick up browned bits and bring mixture to a low simmer. Once simmering, add 1 tablespoon of flour to the mixture and whisk to incorporate until no lumps remain. Add the capers at this time as well.
Carefully put chicken back into the skillet and allow to simmer with the cream sauce for 7-10 minutes, spooning the sauce over the chicken throughout the cooking process.
Once chicken is done and cream sauce is nice and thick, remove from heat and allow to cool a little before serving. Garnish with fresh parsley (optional).