Want to increase my BMI in a healthy way?

Resistance training. BMI just reflects the amount of body mass per unit of height. Increasing muscle mass is the one dependable way to do so in a healthy way. You can't increase your bone structure and fat is not a desired add on. Isometrics, resistance bands, free weights or machines, etc. will all help you tone up and potentially add to lean muscle mass.
See glycemic index. To me the glycemic index and load are perfect for this objective. By eating up to 5 meals per day, 3 larger and 2 smaller snacks, one can reduce the abount of Insulin in your blood stream leading to loss of weight.