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In a medium saucepot over medium-high heat, bring 3 cups water, the milk, 1 teaspoon salt and some pepper to a boil. Gradually whisk in the polenta, whisking constantly until the mixture is smooth and begins to thicken.
Reduce the heat to medium-low and cook, stirring often, until tender and thickened but still creamy, about 30 minutes, adding more water if needed. Stir in the Parmesan and butter. Remove from heat and keep warm.
Heat the remaining 3 tablespoons oil in a large high-sided saute pan over high heat. Add the onions and cook for 3 minutes. Add the garlic and cook, stirring occasionally, until aromatic, about 1 minute. Add the mustard greens, tossing to coat. Add a few drops of honey and then season with salt and pepper.
Reduce the heat to medium, stir in 1 cup water, then cover and cook until wilted and soft, about 10 minutes. Remove the lid and cook and additional 5 minutes to cook off any extra liquid. Stir in the vinegar just before serving. Taste, and season with more honey, salt and pepper if necessary.