Prep the oven. Preheat the oven to 400°F. Lightly brush a 9×13-inch baking dish with the melted butter.: The warm, buttery scent signals the oven is ready and sets up the dish for even browning. You should feel a gentle heat when you open the oven, and the preheated environment helps the taquitos crisp evenly as soon as they go in. The brushed butter prevents sticking and encourages golden bottoms. A common mistake is placing an un-preheated pan into the oven which delays crisping, so always preheat fully until the oven reads 400°F.
Cook the chicken. In a large skillet, melt 1 tablespoon of the butter and add the chicken to it. Season the chicken with half the fajita seasoning and toss to coat. Cook the chicken for about 5 minutes until it's no longer pink, and it's slightly charred, but not burned. Remove chicken from skillet, and wipe the skillet clean.: As the chicken sizzles, you will hear a gentle sear and smell a toasty, savory aroma that indicates the surface is caramelizing. The slight charring deepens flavor without drying the meat, and tossing helps every piece pick up seasoning. Wiping the skillet removes browned bits that could burn the vegetables, creating a clean surface for the next stage. Avoid using too high heat, which can char the exterior before the inside cooks through.
Cook the veggies. Add the remaining 2 tablespoons of butter to the skillet and melt. Add the onion and peppers, season with remaining fajita seasoning and cook for a couple minutes until the onion peppers soften and the onion becomes translucent.: The pan will fill with sweet, savory steam as the onion and bell peppers release moisture and begin to soften. You want softened vegetables with slightly joyous edges but still some snap in the peppers, which keeps textural contrast. The remaining fajita seasoning brings a unified flavor, blooming in the butter and coating the veggies. Overcooking here makes the filling too soft, so stop when translucency appears and peppers give slightly to a fork.
Assemble the taquitos. Lay a tortilla flat on a cutting board and top with some chicken fajita mixture, and a couple tablespoons of cheddar cheese. Tightly roll up the tortilla and place it in the prepared baking dish. Repeat with remaining tortillas. Brush the taquitos with melted butter.: As you roll, you will notice the warm filling steam a bit and the cheese begin to soften, helping it bind. Rolling tightly is key to keep the filling inside, and placing seam side down helps them stay closed while baking. The final brush of melted butter ensures the exterior browns and becomes crisp. A frequent slip is overfilling, which makes rolling difficult and causes leaks, so measure filling consistently for each tortilla.
Bake. Transfer the baking dish to the preheated oven and bake for about 15 minutes or until tortillas are nicely golden brown. If they're still not golden after the 15 minutes, turn the broiler on and broil them for 1 to 2 minutes until golden, watching it carefully to not burn.: While baking you will see the edges take on a warm, golden color and the cheese inside will soften and meld. The oven's dry heat draws out surface moisture so the tortillas crisp rather than steam. If you choose to broil briefly, the color comes quickly, so stay attentive and listen for the faint crackle that signals browning. A common error is leaving them unattended under the broiler, which can quickly go from golden to burned, so watch closely and remove when color is right.
Ready to serve. Serve with salsa and/or sour cream.: The finished taquitos should offer a crisp exterior and a warm, flavorful interior with melty Mexican cheese blend and seasoned chicken . Serving with salsa or sour cream adds a bright or cool counterpoint that complements the rich filling. If the taquitos sat a bit, reheating in a hot oven for a few minutes refreshes the crispness. Avoid microwaving for reheating unless you plan to crisp them afterward, because the microwave will make tortillas soggy.