Preheat the oven to 300 degrees . In a large, heavy ovenproof pot or Dutch oven, cook the bacon over medium, 5 minutes. Stir in the onion and 2 tsp. sugar. Cover and cook over medium, stirring occasionally, until the onion is deep brown, 12 to 14 minutes. Stir in the beer, scraping up any browned bits from the bottom of the pan.
In a bowl, combine the beef, allspice, 3/4 tsp. salt and 1/2 tsp. pepper. Transfer to the pot along with the parsnips, bay leaves, mustard, 1 tbsp. thyme and the remaining 1 tsp. sugar; bring to a simmer over medium. Cover, transfer to the oven and cook until the beef and parsnips are tender, about 1 1/2 hours; remove the bay leaves and season. Divide among bowls; sprinkle with the remaining thyme.