Combine the molasses, water, vinegar, mustard, honey, and salt and pepper, to taste, in a medium bowl. Slowly whisk in the oil until emulsified.
Heat the oil in a large saute pan over medium-high heat until it begins to shimmer. Add the onion and carrot and cook until soft, about 4 minutes. Add the garlic and jalapeno and cook for 30 seconds.
Add the beans and lobster and cook until slightly heated through, about 2 minutes. Transfer to a serving bowl, add the dressing and parsley and toss to coat. Let sit at room temperature for 30 minutes before serving to allow flavors to meld.