Whisk butter, then sugar, then sour cream into cooked cornmeal until combined. At this point, the wet mixture should be cool enough that adding the eggs will not scramble them, but if it still seems too hot, let it cool for 5 minutes longer. Whisk in eggs until combined.
Fold in flour mixture until thoroughly combined and the batter is very thick. Divide batter evenly among prepared muffin cups; it will mound slightly above the rim.
Bake until tops are golden brown and toothpick inserted in center comes out clean, 13 to 17 minutes, rotating muffin tin halfway through baking to ensure even cooking. Let muffins cool in muffin tin on wire rack for 5 minutes, then remove muffins from tin and let cool 5 minutes longer. Serve warm with honey butter or just honey if you feel guilty.
Eat by themselves, with Chili, with just about anything.