In a saucepan with a lid, mix the stock and coconut milk. Bring to a simmer, covered, over low.
Season the pork with salt and pepper. In a deep, medium nonstick skillet, heat 1 1/2 tsp. oil over medium-high. Add the pork and cook, stirring occasionally, until browned, about 3 minutes. Add 1 1/2 tsp. curry paste and cook, stirring often, until the pork is cooked through, about 2 minutes. Transfer to a small bowl.
In the skillet, heat the remaining 1 1/2 tsp. oil over medium. Add the shallot; cook, stirring often, until softened, about 2 minutes. Stir in the rice, then the mirin and the remaining 1 tbsp. curry paste. Cook, stirring often, until the liquid is almost evaporated, about 30 seconds.
Add 1 cup stock mixture. Cook, stirring, until almost absorbed, 2 to 4 minutes. Continue adding the stock by the cup, stirring between additions, until the liquid is almost absorbed and the rice is al dente, about 18 minutes total. During the last few minutes of cooking, stir in the pork, spinach and lime juice. Top with the herbs and lime zest.