In a skillet over medium heat, warm 1 tablespoon of the olive oil and the butter. Add the bread cubes and a generous sprinkle of salt. Toss the bread until crisp around the edges but still chewy inside, about 5 minutes. Remove from the skillet and set aside.
In a large bowl, combine the radishes, peas, beans, and bread cubes.
In a small jar with a lid, combine the garlic, lemon zest and juice, vinegar, ¼ cup olive oil, oregano, salt, and pepper. Shake to combine.
Pour dressing over salad. With clean hands, toss everything together until well combined. Let sit for at least 30 minutes.