Prep the radishes by removing tops and roots. Slice in half lengthwise and set aside.
In a skillet, heat butter over medium low heat. Add in scallions and let cook until beginning to soften, 2-3 minutes. Add the radishes, thyme, and salt to the scallions. Cover and let cook, stirring once or twice, until radishes are tender but still have a bit of crispness to them, 5-6 minutes. Taste and adjust seasoning.
While radishes cook, poach eggs. I find I have the best luck with this technique. If you don't like runny eggs, this would also be great with scrambled or hardboiled.
To serve, place toast on two plates, divide radish mixture, and top each with a poached egg.