How to Make It
Melt the butter in a saucepan. Add the ginger and garlic and cook over moderately high heat, stirring, until fragrant. Add the vinegar and cinnamon stick and cook until reduced to a glaze, about 1 minute. Stir in the tomatoes, sugar, cumin, cayenne and cloves. Reduce the heat to low and cook, stirring occasionally, until the liquid has evaporated, about 1 hour. Discard the cinnamon.
Stir in the honey and season with salt and black pepper. Transfer the mixture to a food processor and puree until smooth. Let cool.
Light a grill or preheat the broiler. In a medium bowl, coat the shrimp with the tomato jam and let marinate at room temperature for 30 minutes.
Grill the shrimp for about 2 minutes per side, or until lightly charred on the outside and opaque throughout.