Preheat the oven to 350 degrees F. Bring a large pot of salted water to a boil. Add the broccolini; cook until tender, about 3 minutes. Drain, then blot dry with paper towels and let cool, 5 minutes.
Transfer the broccolini to a food processor and pulse until finely chopped. Add the cream cheese, mayonnaise, sour cream, 1/2 cup parmesan, the lemon zest, hot sauce and garlic; pulse until smooth. Transfer the mixture to a bowl and fold in the artichoke hearts, havarti, dill and all but 1 tablespoon of the scallions. Transfer to a 1-quart baking dish and top with the remaining 1/4 cup parmesan.
Bake until lightly browned and bubbling, 25 to 30 minutes. Top with more dill and the reserved scallions.