Heat the oil in a medium saucepan over medium heat. Add the red onion and ginger and sauté for 3–4 minutes, until the onion begins to soften.
Add the cumin, garam masala, chili powder, mustard powder, and turmeric. Cook for about 30 seconds, stirring constantly, until the spices are fragrant.
Add the diced mango, cinnamon stick, brown sugar, apple cider vinegar, and salt. Stir until everything is well combined.
Bring the mixture to a gentle simmer, then reduce the heat to low. Cook uncovered for 20–25 minutes, stirring occasionally, until the mango is tender and the chutney has thickened. As it cooks, gently mash some of the mango with the back of a spoon while leaving plenty of pieces intact for a chunky texture.
Remove the chutney from the heat and discard the cinnamon stick. Stir in 1 tablespoon fresh orange juice. Taste and add the remaining tablespoon if you’d like a brighter, slightly sweeter citrus finish.
Let the chutney cool before serving. It will continue to thicken as it cools.