In a large bowl, whisk together tamari or soy sauce, balsamic vinegar, and olive oil. Add broccoli florets and toss until they are well coated. Season with a pinch of kosher salt.
Place the broccoli in a grill basket or directly on the grill grates, ensuring they are in a single layer. Grill the broccoli, turning occasionally, until they are charred at the edges and tender, about 10 to 12 minutes.
Remove the broccoli from the grill, drizzle with a bit more olive oil, and garnish with chopped parsley. If desired, finish with a sprinkle of flaky sea salt. DEVOUR!