Heat oil in a Dutch oven over medium heat until shimmering. Add onion; cook, stirring occasionally, until softened and just starting to brown around edges, about 4 minutes. Add garlic; cook, stirring constantly, until fragrant, about 45 seconds.
Stir in chickpeas, tomato sauce, pepper, oregano, crushed red pepper and salt; cook, stirring often, until the chickpeas are warmed through, about 2 minutes. Add vodka sauce; cook, stirring occasionally, until steaming, about 2 minutes.
Add half-and-half; bring to a simmer over medium heat. Stir in kale; cook, stirring constantly, until wilted and bright green, about 1 minute.
Divide among 4 shallow bowls; top each with 2 tablespoons Parmesan. Serve each with 2 toasted baguette pieces.
