Heat oven to 375°.
If you're using greens, cut them from bunch of radishes and wash well in cool water, as you would salad greens. Once they're hiding no more grit, spin them dry in a salad spinner.
Put a small slick of olive oil in a large ovenproof skillet and heat over medium-high heat. Arrange radishes cut side down and cook until lightly browned, about 3 minutes. Transfer to oven and roast until radishes are nicely browned and starting to get tender, about 10 minutes*.
Add radish greens and roast until radishes are fully tender and greens have wilted, another 5 minutes.
Take skillet from oven and set over low heat on the stove (careful, the handle is hot!). Season nicely with salt, black pepper, and 1/2 tsp. chile flakes. Add butter and cook until butter has melted and is starting to get golden brown and nutty smelling, 2 to 3 minutes.
Add vinegar to skillet and gently fold everything to combine. Drizzle on honey and fold again. Taste and adjust seasoning with more salt, black pepper, chile flakes, vinegar, or honey. Serve warm.
*Ideally, use small radishes. Cooking times may be longer for larger radishes.