In regard to grilling...
- High levels of protein, especially animal protein, when grilled over a high heat and allowed to become dry, can create Heterocyclic Aromatic Amines, which are carcinogens. This is one of the reasons why they recommend to marinate animal protein before grilling as it reduces the amount of HCAA's formed.
- High levels of fat, have a two fold problem. 1) heating fat can cause one type of carcinogen (lipid peroxides) and 2) when fat drips down into the hot coals, it creates another carcinogen, that then rises back up into the meat.
- Charring food, creates another type of carcinogen.
Most plant foods have neither of the first two issues so are safe to grill, just don't char them.