Using a meat mallet, flatten the tenderloins to even thickness. Set up three bowls for dredging: one with flour, one with beaten eggs, and one with a mixture of breadcrumbs, lemon zest, and cheese. Coat each tenderloin first in flour, then in egg, and finally in the breadcrumb mixture.

Heat olive oil and butter in a large nonstick sauté pan over medium heat. Once hot, fry the chicken on both sides until golden and cooked through, about 3-5 minutes per side. Work in batches if necessary. Drain on paper towels.

In a medium saucepan, heat olive oil over medium heat and sauté garlic until fragrant. Whisk in flour, then gradually add milk, cream, and chicken broth. Increase heat to medium-high, bring to a boil, and cook until the sauce thickens, about 3-5 minutes.

Remove from heat and stir in lemon juice and butter. Drizzle sauce over chicken before serving.