Toss radishes, cucumbers and vinegar in a medium bowl; season with salt. Let marinate until ready to use.
Thinly slice 8 scallions. Melt butter in a medium pot over medium heat until foaming. Add ginger, garlic and sliced scallions and cook, stirring often, until tender and golden, 8-10 minutes.
Stir in steel cut oats and cook, coating the oats in the aromatics until warmed through, about 2 minutes.
Add the broth and increase heat to high and bring the mixture to a boil, then reduce heat to medium-low and cook, stirring occasionally, until the oats are tender, and the liquid is thick and creamy, about 30-35 minutes.
Slice remaining scallions on a diagonal angle and toss with pickled vegetables.
Divide oats among bowls. Arrange crunchy veggies on top and drizzle with any liquid that remains in the bowl.