Add flour, salt, black pepper, and garlic powder to shallow dish. Whisk ingredients together until evenly distributed.
One by one, dredge chicken cutlets through flour mixture. Make sure to evenly coat all sides of each cutlet. Shake any excess flour mixture back into dish, then set breaded cutlet aside and repeat until all cutlets have been lightly breaded.
Once all cutlets have been breaded, heat large skillet over medium-high heat. When skillet is warm, add olive oil and heat until oil is hot and shimmering.
Add chicken cutlets to skillet, working in batches as needed to avoid overcrowding pan. Cook cutlets 3 to 4 minutes undisturbed, then carefully flip cutlets over and cook 3 to 4 additional minutes or until cutlets are golden brown on both sides. Transfer cooked cutlets to clean plate and set aside. Repeat process until all cutlets have been pan-fried. Note: refresh olive oil in pan as needed, allowing fresh oil to become hot before adding cutlets.
Once all cutlets have been pan-fried and set aside, reduce heat under skillet to medium. Add 2 tablespoons butter to skillet. Let butter melt completely, swirling skillet occasionally to coat bottom in butter. Be careful not to burn butter.
Add sliced almonds to melted butter. Cook, stirring occasionally, 2 to 3 minutes or until almonds are just lightly browned. Note: almonds can burn easily so be careful not to overcook.
Add chicken broth, lemon juice, and lemon zest to skillet with almonds. Stir to incorporate, then bring sauce to boil. Once sauce begins to slowly boil, reduce heat to low and stir in fresh chives and fresh parsley to taste.
Return chicken cutlets to skillet and spoon sauce over. Simmer sauce and chicken until sauce has thickened and chicken is warmed through. Garnish with additional chives and parsley if desired and serve warm with preferred sides.