Slice Eggplant to 1/3 inch thick pieces and brush with olive oil.
Slice halloumi into 1/2 inch thick pieces, brush with olive oil.
Slice tomatoes into ½ inch slices, set aside.
Make dressing. Blend or process all ingredients in a blender or food processor adding a little more water (only if necessary) to get the blender going. Do not blend it too smooth you want to see pieces of the herbs.
Grill eggplant slices, closing lid, checking heat to make sure they don’t burn, rotating as necessary. Eggplant is done when the white becomes slightly translucent. Stack them on a heat proof dish and cover tightly with foil so they continue cooking through. You could place this on your upper grill rack if you have one, or just set aside, covered.
Grill the Halloumi cheese just until grill marks appear.
Arrange eggplant, tomatoes and cheese all on a platter, layering. Drizzle liberally with the dressing and a sprinkle of salt and pepper, and garnish with fresh mint leaves. Serve at room temp.
If you want to serve this Napoleon Style- a stacked individual portion, layer eggplant, tomato, and haloumi spooning a little mint dressing on each layer, until 4-5 inches tall. Skewer with a skewer or sturdy rosemary sprig ( removing bottom rosemary leaves).