Mix all the chimichurri ingredients in a blender until smooth. Reserve in the refrigerator for up to a month.
On a long, cocktail-sized bamboo skewer soaked in water for 30 minutes, thread the tomato, then halloumi, and repeat.
Transfer the skewers to a baking sheet, brush each with Greek chimichurri.
Heat a grill to medium-high heat. Place the baking sheet with the skewers directly on the grill.
Carefully flip occasionally, until the cheese begins to melt and char and the tomatoes are about to burst, 3 to 5 minutes.
Remove from the heat and transfer to a serving dish. Drizzle with more Greek chimichurri, garnish with small oregano leaves, finely chopped chives, sorrel, or torn mint, and serve immediately.
