Preheat the oven: Preheat your oven to 425°F and line a large baking sheet with parchment paper for easy cleanup.
Season the squash: Toss the sliced delicata squash with 2 tablespoons olive oil, smoked paprika, half the salt and half the pepper until evenly coated.
Roast until golden: Spread the squash in a single layer on the baking sheet and roast for 18-20 minutes, flipping halfway, until the edges turn golden brown and the squash is fork-tender.
Whisk the dressing: In a small bowl, whisk together mayonnaise, Greek yogurt, lemon juice, Dijon mustard, soy sauce, rice vinegar, minced garlic and grated Parmesan until smooth and creamy.
Season the dressing: Taste the dressing and add the remaining salt and pepper as needed, adjusting lemon juice for brightness.
Dry the romaine: Chop the romaine into bite-size pieces and spin or pat it dry so the dressing coats the leaves instead of sliding off.
Combine the salad: Add the romaine to a large bowl, pour the dressing over the top, and toss gently until every leaf is lightly coated.
Add warm squash: Fold in the warm roasted squash and croutons carefully so the squash pieces stay intact.
Add chicken if using: If adding protein, fold in the shredded rotisserie chicken now for a heartier main-course salad.
Top and serve: Finish with shaved Parmesan cheese and a final crack of black pepper, then serve immediately while the squash is still warm.