Deseed the tomatoes by cutting them in quarters and then cutting out the core, then dice them.
Heat a medium saucepan and over low heat, sauté the onions until they become soft and slightly translucent (about 10 minutes). Add water a tablespoon at a time if they begin to stick.
Add the minced garlic and sauté for another minute.
Add the tomatoes, 1 Tbsp. mustard, 1 tsp. Agave syrup and ½ cup rice wine vinegar. Bring the heat up to medium, cover and simmer until the tomatoes are reduced and the chutney is thick. This takes about 45 minutes to 1 hour. Stir it occasionally.
Once the chutney is sufficiently reduced (to about half of where you started) and has a consistency you like, remove it from the heat and allow it to cool a few minutes before mixing in the chopped basil.
Serve warm or cold.
Store in a sealed container. Keeps for a week in the fridge.
You can substitute canned tomatoes for fresh. Drain them before using. Otherwise the reduction process will take forever. Your canned tomatoes make be a bit sweeter than fresh, so consider adjusting the amount of sweetener.
As noted above you can use dry basil. Use 1 ½ tablespoons and simmer the dry basil along with the tomatoes.
The chutney may settle once it has cooled. Just give it a stir to liven it back up.