Trim the greens and root ends from the radishes. Gently smash each radish with a meat mallet (or the side of a knife) until it cracks but stays mostly intact.
Place radishes in a bowl, sprinkle with 1 tbsp kosher salt, and toss to coat. Let sit for 30 minutes to draw out moisture.
Rinse and drain the radishes well, then transfer to a large glass jar with a lid.
In a small pot, combine the rice vinegar, water, sugar, soy sauce, garlic, sriracha, sesame oil, white pepper, and remaining 1 tsp kosher salt.
Bring the brine to a simmer over medium-high heat, stirring until the sugar dissolves. Remove from heat and let cool slightly.
Pour the brine over the radishes, cover, and refrigerate overnight. Shake the jar once or twice if the brine doesn't fully cover the radishes.
Serve the pickled radishes with sliced scallions if desired. Store in the refrigerator for up to 3 weeks.
