In a medium pot over medium heat, melt 2 tablespoons of butter.
Add the onion and saute until tender, about 10 minutes, then add the GGP and cook for 5 minutes more, stirring often.
While the GGP cooks, rinse the rice in a fine-mesh strainer until the water is clear. Add the rice to the pot and cook, stirring often, until toasted, about 5 minutes.
Add the remaining ingredients and 1 tablespoon butter. Bring the mixture to a boil over high heat, stirring occasionally to prevent sticking, then reduce heat to low and cover. Cook until the liquid has been absorbed, 18 minutes.
Remove the pot from heat and let rest, covered, for 5 minutes, then uncover.
Remove and discard the thyme, ginger, bay leaf, and Scotch bonnet (being careful not to puncture it). Fluff with a fork and let sit uncovered, 5 minutes more.
Fold in the remaining tablespoon of butter and season to taste with salt.