Whisk the dressing ingredients, olive oil, lemon juice, honey, salt, and pepper, in a small bowl or jar. Set aside.
Deseed the pomegranate, slice the cucumber, thinly slice the red onion, and chop the mint and parsley.
Pat the halloumi slices dry with paper towels. Dry cheese browns better and splatters less in the hot oil.
Heat 1 tbsp olive oil in a 10-inch nonstick skillet over medium-high. Once the oil shimmers, add half the halloumi slices in a single layer without overlapping.
Fry for 2 to 3 minutes per side, until deep golden brown with a light crust. Transfer to a paper towel-lined plate. Add the remaining oil and repeat with the second batch of halloumi.
In a large mixing bowl, toss the salad greens, cucumber, onion, mint, and parsley with half the dressing.
Divide the dressed greens among plates. Top with the warm halloumi slices, scatter over the pomegranate seeds and walnuts.
Drizzle with the remaining dressing and serve right away while the halloumi is still warm and crisp.