Talk to the tenant and let them know about your concerns about being significantly below market and let the tenant know that you intend to change your process/structure. Let the tenant know that you want to increase the rent by 10% this year, but also provide some sort of range that you'd like to increase the rent by in order to keep up with the market, account for property tax increases and some of those major expenses.
One of three situations should happen. Situation 1, tenant sticks around for the 10% increase and accepts the future increases. Situation 2, tenant takes the 10% increase, but moves out after the year. Situation 3, tenant moves out immediately when you try to increase the rent even by 10%.
Outcomes for each. Outcome 1, you get to keep your great tenant and gradually increase your rent like you'd like to. Outcome 2, you increase rent by a fraction for year 1 and have the opportunity to increase to market value after year 1 with a new tenant. Outcome 3, you get to increase rent and get to market immediately with a new tenant.
Open lines of communication with tenants are always preferred. Don't be afraid to talk to your tenant and work collaboratively to come up with a solution that works for both of you.