Reduce heat to medium and add the chopped onion and thyme and continue cooking until translucent. Add the rice and stir for 1-2 minutes (at this stage you should be careful not to burn the onion). Add the white wine with the porcini.
When the wine evaporates start adding the stock, half a cup at a time. Reduce to medium-low and simmer gently.
After adding about 6 cups of stock, add the milk, salt and pepper.
Turn off the heat. It will continue to cook for a while until you serve it.