Make the anchovy butter: Add the softened butter, finely chopped anchovies, chives, and a small pinch of flaky sea salt to a bowl. Mash together with a fork until well combined.
Toast the sourdough: Lightly brush both sides of the sourdough with olive oil. Toast in a skillet over medium heat for 2–3 minutes per side, until golden and crisp.
Assemble: Spread a generous layer of anchovy butter over each piece of warm sourdough.
Add the radishes: Arrange the thinly sliced baby radishes over the anchovy butter.
Finish: Drizzle the radishes with fresh lemon juice and top with more chopped chives and flaky sea salt. Serve immediately.