bake, roast, toast, cook
烤 centers on applying dry heat to food: baking, roasting, toasting, or cooking with fire.
烤 combines 火 (fire) with 考, which likely contributes the sound. The character is a relatively modern formation for cooking with fire.
The left side is fire 火, and the right side is 考, which looks like an old person leaning on a cane. Picture an old person carefully tending a fire to bake bread.
For コウ, imagine a coal fire baking food: coal -> コウ, and the fire 火 on the left provides the heat.