Preheat your oven to 350°F (175°C). In a food processor, blend together the all-purpose flour, powdered sugar, salt, and butter until the mixture resembles fine crumbs. Press this crumbly goodness evenly into the bottom of an 11×7-inch baking pan, ensuring it's compact. Bake in the preheated oven for 18-20 minutes, until it turns a delightful golden brown.

While the crust is baking, grab a mixing bowl and whisk together granulated sugar and a touch of flour. Carefully add the eggs one at a time, mixing thoroughly after each addition. Next, stir in the vibrant lime zest and fresh lime juice, along with food coloring if desired. Whisk until smooth, ensuring no lumps remain in your creamy filling.

Once the crust is done and golden, remove it from the oven and immediately pour the lime filling over the hot crust. Return the pan to the oven and bake for an additional 18-20 minutes. Keep an eye on it; the filling should be set and no longer jiggle in the center when you gently shake the pan.

After baking, allow your lime bars to cool in the pan for about an hour. Once cooled, place the pan in the refrigerator and let the bars chill for 1-2 hours. This step is vital as it helps the bars firm up, making them easier to cut. Use parchment paper edges to lift them out for clean slicing.