Place a boneless, skinless chicken breast (with the tender removed) on a cutting board and hold it flat with the palm of your non-dominant hand. Slice the chicken breast horizontally into two even pieces. Repeat with the remaining chicken.
Cover the chicken with parchment paper or plastic wrap. Use a meat mallet or the bottom of a heavy skillet to pound the chicken until it is an even thickness. Season both sides evenly with salt and pepper.
Set 2 tablespoons of the cassava flour aside (you will use this in to make the roux later.) Pour the remaining cassava flour into a wide bowl (it's about 6 tablespoons total) and lightly dredge both sides of each cutlet into the flour until evenly coated, then shake off any excess. Place all the dredged cutlets on a clean plate and set aside.
Heat the oil a large skillet set over medium-high heat. Working in batches so as to not overcrowd the skillet, carefully add the cutlets and cook until a golden crust has formed on each side, about 2 minutes per side. Transfer the browned cutlets to the bottom of the Crockpot. They don’t have to be completely cooked through.
Melt the butter in the same skillet over medium-low heat. Stir in the reserved 2 tablespoons of flour and cook until a loose paste forms. Add the garlic cloves and cook, toasting the flour a bit so it doesn’t have a raw flavor, 1 to 2 minutes, being careful not to burn.
Slowly pour in the chicken broth, whisking constantly, until a roux forms. Bring the mixture to a light simmer until it turns into a thin gravy, 3 to 4 minutes (it will continue to thicken in the Crockpot).
Stir in the lemon juice and capers. Pour the sauce over the chicken in the Crockpot. Cover and cook on low for 4 to 6 hours.
Garnish with chopped fresh parsley and serve!