Prepare the salad: Heat oil over medium-high in a medium saucepan and add berkoukes (see Tip). Stir until the pearls begin to brown and smell toasty, about 3 minutes. Add ¾ cup water and ¼ teaspoon salt and bring to a boil. Cover, adjust heat to medium-low and simmer 10 to 15 minutes, until tender. (The timing might vary depending on the brand.) Drain if any liquid remains in the pan and leave to cool at room temperature. Fluff with a large spoon to separate the pearls.
While the berkoukes cooks and cools, make the dressing: In a small bowl, mix to combine the oil, vinegar, honey, oregano, ¼ teaspoon salt and 1 large pinch pepper. Taste and adjust seasoning as desired.
Finish the salad: To a large salad bowl or shallow platter, add the arugula, cilantro, parsley and mint; toss to combine. Add the cooled berkoukes, plus the peaches, tomatoes, olives, almonds, red onions and the dressing; toss to combine. Garnish with more almonds and serve.