Whisk together the half and half, chicken broth, hot sauce, Dijon mustard, soy sauce, onion powder, oregano, basil, parsley, and garlic salt in a large measuring cup with a spout, then measure the remaining ingredients before you start cooking. The sauce mixture should look fully blended so it pours evenly into the skillet later.

Heat the olive oil in a large skillet over medium-high heat, add the ground sausage, and cook for about 7 minutes while breaking it into crumbles, then transfer it to a plate and turn off the heat. The sausage should be cooked through, browned in spots, and sizzling as it finishes, with a rich garlic-and-sausage style aroma already building in the pan.

Bring a separate pot of well-salted water to a boil for the pasta while you work on the sauce base. Getting the water going now keeps the timing smooth and helps dinner come together without a last-minute scramble.

Pour the white wine into the same skillet, set the heat to medium, and scrape up the browned bits from the bottom with a silicone spatula, then let the wine reduce for about 4 minutes. The pan should smell deeply savory and the liquid should look slightly reduced, not watery.

Stir in the minced garlic and cook for 1 minute, then add the butter and gradually sprinkle in the flour while stirring constantly for 1 to 2 minutes. The mixture should look smooth and paste-like, and the raw flour smell should disappear.

Add the shell pasta to the boiling water and cook by timer, then add the broccoli during the last 3 to 5 minutes if using fresh or the last 2 to 4 minutes if using frozen, and drain when both are tender. The broccoli should stay bright and crisp-tender rather than soft and faded.

Pour the prepared sauce mixture into the skillet in small splashes, stirring the whole time, then bring it to a boil and lower the heat to low. Adding the liquid gradually helps the sauce stay smooth, and it should thicken enough to coat the back of a spoon instead of looking thin.

Stir in the softened cream cheese, then add the grated Parmesan a little at a time, stirring until smooth, and partially cover the skillet while the pasta finishes. The sauce should look creamy and clingy, not grainy or separated, and it should not pool heavily at the bottom of the pan.

Add the drained pasta, broccoli, and cooked sausage to the skillet, toss until everything is coated and heated through, then remove from the heat and stir in the fresh lemon juice. The finished pasta should look glossy and creamy, with the sauce clinging to the shells and the lemon lifting the whole pan at the end.