Heat olive oil in a large saute pan or dutch oven over medium-high heat. Add jalapenos, carrots, garlic and onion. Saute for 10 minutes, stirring occasionally.
Add the remaining ingredients to the pan, mix together and bring to a boil. Lower heat and simmer for 10 minutes.
Remove from heat and place vegetables in an airtight container (I like these glass jars{affiliate link}). Cover vegetables with cooking liquid and let sit on the counter to cool to room temperature. Once cooled, store in the fridge for up to 1 month.
Notes
Don't have whole black peppercorns? That's okay. You can leave them out of the recipe and it won't affect the flavor too much.