Cook the orzo according to the instructions on the package, then rinse it under cold running water until it no longer feels warm. Drain completely.
While the orzo is cooking, make the dressing: combine all the ingredients in a small bowl or glass measuring cup; whisk vigorously until well combined and slightly emulsified. Set aside.
Combine the drained orzo, thawed green peas, chopped cucumbers, sliced green onions and chopped parsley in a large bowl. Add the dressing and toss until well combined. Divide the salad equally between 4 bowls and reserve. You can also refrigerate the salad at this point to serve at a later time.
When ready to eat, heat a well oiled cast-iron grill pan over medium-high heat and grill the slices of halloumi cheese until golden brown, about 45 seconds per side. Top each salad with 2 to 3 slices of warm cheese.
Garnish with thin slices of cucumber and fresh thyme, if desired and serve without delay.