Kimchi Grilled Cheese

2 tablespoons canola oil
8 whole-wheat bread slices
3 ounces thinly sliced fresh mozzarella cheese
1 1/2 ounces (1/3 cup) shredded Monterey Jack cheese
2 tablespoons chopped kimchi

Brush canola oil evenly over 1 side of whole-wheat bread slices.
Arrange 4 bread slices, oiled side down, on a work surface.
Divide thinly sliced fresh mozzarella cheese and shredded Monterey Jack cheese evenly among arranged bread slices;
top each with 2 Tbsp. chopped kimchi and 1 bread slice, oiled side up.
Cook sandwiches in a large nonstick skillet over medium-high until toasted and cheese is melted, about 3 minutes on each side.