Make the chili jam first: in a 1-quart / 1L saucepan, combine the tomato paste, honey, rice vinegar, soy sauce, garlic, chili flakes, and water.
Simmer over medium-low heat for 5 to 6 minutes, stirring often, until the mixture coats the back of a spoon like jam. Remove from heat, it thickens more as it cools.
Pat the halloumi block dry with paper towels and cut into fries about 1 cm / 1/2 inch thick and 6 cm / 2.5 inches long, you should get about 12 fries.
Set up two shallow bowls: beaten egg in one, cornstarch mixed with black pepper in the other.
Dip each halloumi fry in egg, then roll in the cornstarch mixture, pressing gently so it coats all sides. Shake off any excess.
Heat the olive oil in a 10-inch / 25 cm nonstick skillet over medium heat until it shimmers.
Add half the fries in a single layer, don't crowd the skillet. Fry for 2 to 3 minutes per side, turning with tongs, until deeply golden on all sides, 6 to 8 minutes total. Repeat with the second batch.
Transfer the fried halloumi to a paper towel-lined plate to drain briefly.
Arrange the fries on a plate, drizzle with some of the chili jam and set the rest in a small bowl for dipping.
Scatter the chopped cilantro over the top and serve with lime wedges.