For the chutney: Combine the tomatoes, vinegar, brown sugar, coriander, ginger, red pepper flakes, shallots, garlic and 1 teaspoon salt in a medium saucepan. Bring to a boil over high heat, then reduce the heat to keep at brisk simmer. Cook, stirring often, especially towards the end, until thickened and jammy, 30 to 35 minutes. Cool to warm or room temperature.
For the crackers: Meanwhile, preheat the oven to 350 degrees F. Line a sheet pan with parchment paper.
Whisk the egg white, rosemary, salt and pepper together in a large bowl until frothy. Add the almond flour and Parmesan. Mix well to form a dough.
Flatten the dough into a rectangle and sandwich between 2 sheets of parchment paper. Roll the dough out into an approximate 10-inch square, patching up any cracks with your fingers as you go. Use a sharp knife or pizza cutter to cut the dough into approximate 1 1/2-inch squares. Transfer to the lined sheet pan and bake until golden brown and crisp, 15 to 20 minutes, then transfer the crackers to the cooling rack and cool completely (crackers along the edge may cook faster than those in the center; transfer them to a cooling rack and continue to bake the remaining crackers).
Serve the tomato chutney with the crackers on the side. Any remaining chutney can be kept refrigerated in an airtight container for up to 1 week and is delicious with cheese, on burgers or on a sandwich.