Make the chicken first by patting a thin-sliced breast dry with a paper towel. Season the chicken breast with salt, pepper, onion powder, garlic powder, and lemon pepper seasoning. Next, heat the olive oil on medium-high heat in a pan on the stove. Place the seasoned chicken in the pan, cooking it on one side until the spices blacken. Flip the chicken over and cook on the remaining side until it’s done, adjusting the heat as necessary to avoid burning. When the chicken is cooked, transfer it to a cutting board to cool temporarily.
Return your used pan to the stove. On low heat, melt the butter in the pan to lift up any leftover spices from the chicken. Once the butter is melted, stir the paleo flour into the pan until it turns golden and frothy. Next, pour the chicken broth into the pan and stir until the flour thickens the broth. Bring up the heat on the gravy until it’s bubbling. Meanwhile, dice your chicken into small pieces.
Transfer the diced chicken to the gravy. Add a sprig of thyme and a small sprig of rosemary to the pan. Place a lid over the pan and let the gravy bubble and thicken around the chicken. After just a few minutes, leave the chicken poutine gravy aside for later. Next, turn the oven on to preheat to 425 degrees and select either a well-seasoned sheet tray or line a tray with parchment paper.
Use a vegetable peeler to peel wide, flat strips from a whole zucchini. Peel until you have enough pieces totaling the weight listed in the ingredients. Lay all the zucchini pieces flat between sheets of paper towels, and press down firmly to extract any excess moisture. Discard the used paper towels and arrange the zucchini on your sheet tray as if the pieces were a big pile of french fries. Spread the pieces out enough to ensure each one will be touched by the chicken poutine.
Pour the chicken poutine gravy over the zucchini on the tray. Make sure you distribute the gravy to ensure even coverage. Crumble chunky pieces of feta cheese over the chicken poutine and set the tray in your oven. Bake the poutine for about 12 minutes. For doneness, look for tender zucchini peels with browned edges and feta crumbles that have mostly maintained their shape but are soft and melted to the touch. Enjoy with a fork and serve hot.