Boil pasta according to directions listed on package adding broccoli during last 3 - 4 minutes of boiling, drain well (reserve 1/4 cup pasta water, just in case you want to thin pasta sauce).: The water should be at a lively boil before adding the large shell pasta , and when you drop it in you'll hear a steady rolling sound as it cooks. Adding the broccoli in the final few minutes lets it cook through while retaining a pleasant crunch and vibrant green color, and you will notice a fresh vegetal scent rise as the florets soften. After draining, shake the colander so excess water releases, and set aside the reserved pasta water in case the sauce tightens later. One common mistake is overcooking the broccoli , which makes it mushy and dulls the color; watch the clock and test a piece for tenderness to avoid this.
Meanwhile, in a pot melt butter over medium heat then stir in flour. Cook mixture stirring constantly for 1 minute.: As the butter melts you'll see it foam slightly and the kitchen will smell rich and buttery. Stirring in the flour right away ensures it absorbs the fat and begins to cook evenly, forming a smooth paste. Cook this mixture for about a minute until it loses the raw flour smell and starts to look slightly glossy, which signals the roux is ready to accept the milk . If you let the roux brown, it will change the sauce color and flavor, so keep the heat moderate to avoid that pitfall.
While whisking vigorously, slowly add in milk, then season with onion powder, garlic powder and salt and pepper to taste. Increase heat to medium-high, cook mixture, stirring constantly until it boils and thickens.: As you pour in the warm milk in a thin stream while whisking, the roux will loosen and the sauce will begin to smooth out, releasing a comforting, creamy aroma. Whisking steadily prevents lumps from forming and helps the mixture become uniform. Once incorporated, add the onion powder, garlic powder, and salt and pepper so the seasonings can bloom in the warm liquid. A typical slip is adding the milk too quickly, which can create lumps; slow incorporation and continuous whisking are the cure.
Remove from heat, allow to cool for 1 minute then add in cheddar and parmesan cheese and stir until melted. Add drained pasta and broccoli and chicken and toss to evenly coat. As it sits it will thicken, you can thin it with a few tbsp pasta water if desired.: The sauce will move from thin and glossy to noticeably thicker as it comes to a gentle boil, and you'll start to see bubbles breaking across the surface with a light simmering sound. Stir constantly so the bottom does not stick and scorch, and watch for the sauce to coat the back of a spoon, which is a reliable visual cue it's thick enough. If you stop stirring, a skin can form on top or it can scorch, so keep it moving to maintain a smooth texture.
Remove from heat, allow to cool for 1 minute then add in cheddar and parmesan cheese and stir until melted: Once off the heat, the residual warmth is ideal for melting shredded cheddar and parmesan gently, producing a silky, cohesive sauce without becoming grainy. The smell will shift to a sharp, cheesy perfume that is instantly comforting. Stir until you no longer see distinct shreds of cheese and the sauce looks glossy; this signals the fats and proteins have emulsified. Adding cheese on too-high heat can make it separate and become oily, so letting the pot cool briefly before adding the cheeses avoids that issue.
Add drained pasta and broccoli and chicken and toss to evenly coat: As you fold the drained large shell pasta , broccoli , and shredded chicken into the sauce, you will notice the sauce clinging to curves and pockets, creating inviting coated shells. The mix of textures is pleasing, with tender chicken pieces and the bright snap of broccoli against smooth, cheesy sauce. If the sauce tightens as it sits, a splash of the reserved pasta water will loosen it to the desired silkiness. A common misstep is combining everything while the sauce is too cool, which prevents proper coating, so ensure the sauce is still warm when you toss.