How to Make It
Heat canola oil in a Dutch oven over medium-high until a thermometer submerged in oil registers 375°F. Add half of farro. Fry until browned and crisp, 4 to 5 minutes (do not allow temperature of oil to drop below 350°F). Remove fried farro from pan with a fine wire-mesh strainer or spider. Drain farro on paper towels; immediately sprinkle with salt to taste. Repeat procedure with remaining farro.
Combine tomatoes, peaches, arugula, onion, and mint in a large bowl. Combine olive oil, vinegar, salt, and pepper in a small bowl or jar; whisk or seal and shake until well blended. Drizzle half of dressing over tomato mixture; toss gently to combine. Arrange salad on a platter; top with burrata pieces and about 2/3 cupfried farro (reserve remaining farro for another use). Drizzle salad with remaining dressing, and serve immediately.
Store remaining fried farro in an airtight container at room temperature up to 1 week or freeze 3 to 4 months.