Char the veggies: Preheat a grill or cast-iron griddle to 350 degrees F.
Place the scallions, jalapeno and onion over the direct heat of the grill, directly on the grates. Cook until charred on one side, then flip to char the second side, 3 to 5 minutes per side. Remove to a cutting board and roughly chop. Set aside.
For the grits: In a large saucepot combine the beef soup base, salt, plenty of pepper and 4 cups water. Bring to a boil, then slowly whisk in the grits. Add the chopped veggies and lower the heat while continuing to whisk. Cook, whisking occasionally, until the grits are thickened, 15 to 20 minutes. Add the heavy cream and butter. Once they are mixed in and the grits are a pouring consistency, add the cheese and whisk until melted and incorporated. Serve warm, topped with additional cheese.