Warm the oil in a medium saucepan set over a medium heat. Add the radishes and cook for 2 to 3 minutes, without shaking the pan, until coloured on one side. Add the shallots and garlic and stir the mixture for 1 minute. Add the balsamic vinegar and honey and cook for 1 minute more to coat the radishes and shallots.
Pour in the warm stock, making sure the radishes are just barely covered with liquid. Cover the pan with a disc of parchment paper or place a loosely putting lid on top. Cook on a very low heat for 5 minutes, until the radishes are softened but still have a bite. Remove the lid and continue to simmer for 3 to 4 minutes, until the liquid has reduced into a syrupy coating sauce. Remove from the heat.
Just before serving, add the parsley and tarragon. Check the seasoning and drizzle with an extra dash of balsamic vinegar. Serve warm.