Melt butter in a medium skillet over medium, stirring constantly, until butter begins to turn golden brown, 4 to 6 minutes. Remove from heat. Pour 3 tablespoons brown butter into a large heatproof bowl, reserving remaining butter in skillet. Return skillet to medium-low heat, and add watermelon radishes and 1 teaspoon of the salt. Cook, stirring often, until radishes are tender, 3 to 4 minutes. Remove from heat; let cool slightly, about 5 minutes.
Add oil, vinegar, honey, mustard, and remaining ½ teaspoon salt to brown butter in large bowl; whisk together until well combined and emulsified. Season with additional salt to taste.
Divide lettuce evenly among 4 plates; top evenly with pecans, pecorino, and radishes. Drizzle each salad with 1 ½ tablespoons dressing; serve remaining dressing on the side.
