Heat canola oil in a medium saucepan over medium heat. Add shallots, garlic, and ginger and cook until aromatic, about 3 minutes. Add in coriander, cinnamon, and salt and mix well for 30 seconds. Stir in agave, vinegar, and water. Add in ground cherries and plums and bring mixture to a boil. Lower heat and let chutney reduce, stirring occasionally, for about 25 minutes.
Once chutney has thickened, transfer to a jar or small bowl and let cool slightly.
For the sandwich:
Butter each piece of bread on one side (about ½ a tablespoon per slice). Place one piece of bread, buttered side down, in a small skillet. Top bread with chutney, about ½ a cup of Gouda, a little bit of arugula, and another piece of bread (buttered side up). Turn heat on medium and press down with a spatula. Cook until bread has started to brown and cheese is melty. Flip and repeat on other side. Repeat with remaining sandwiches.
If you have chutney left over, use it to top pork, chicken, or other sandwiches.