Halloumi is type of Greek cheese that will not melt on the barbecue.
Prepare grill for medium high heat; brush grates with oil.
Make dressing by grated zest from 1 lime, juice from 2 limes, garlic, jalapeno, salt, sugar and whisk until sugar is dissolved; whisk in 1/4 cup oil to emulsify, then stir in capers.
Arrange tomato slices on a large platter.
Halve cheese, diagonally, then cut each half (cut side down) into 3 thin slices; brush cheese with oil and grill until golden and grill marked, about 2 minutes per side.
Spoon dressing over all and top with spicy sprouts.