Toast the mustard seeds and cumin seeds in a dry, heavy-bottomed pan over medium heat for about 1 minute until fragrant and the mustard seeds begin to pop. Immediately remove from heat to prevent burning.
In a large pot, heat 1 tablespoon of olive oil over medium heat. Add the diced onion and sauté for 5-7 minutes until translucent.
Add the ginger and garlic, cooking for another 2 minutes until fragrant.
Add the toasted seeds, chopped chilies, cinnamon, and cloves to the pot, stirring continuously for 30 seconds.
Immediately add the diced mangoes and stir to coat with the spice mixture.
Add the brown sugar, apple cider vinegar, salt, lime zest, and juice to the pot. Stir well until the sugar dissolves completely.
Bring the mixture to a boil, then reduce heat to low and simmer uncovered for 40-45 minutes, stirring occasionally to prevent sticking. The chutney should thicken considerably.
Remove from heat and allow to cool completely. The chutney will continue to thicken as it cools.
Transfer to sterilized jars for storage. For the best flavor development, allow your Mango Chutney to rest for at least 24 hours before serving.