Preheat your oven to 350F and spray or lightly grease a 12-muffin baking pan.
In a large mixing bowl, whisk together the flour, cornmeal, baking powder and soda, and salt.
In another mixing bowl, add your plant milk and vinegar. Allow them to sit for a minute. Then, stir in the sugar and melted butter (or oil and water). Stir these wet ingredients together, then add them to the dry ingredients. Fold everything together with a spatula until just evenly mixed (a few clumps are OK).
Fill your muffin pan about 2/3 of the way with the batter. You'll need enough batter remaining to add a tablespoon on top of each muffin when you finish. Top each partially filled muffin container with a scant tablespoon of jam. Finally, top the jam with another tablespoon (or so) of batter. The muffin pan should be 3/4 full when you're done.
Bake the muffins for 22-24 minutes, or until light golden brown and with set tops. Transfer the muffins to a cooling rack and cool for at least 20 minutes before enjoying. Muffins can be stored in an airtight container in the fridge for up to 3 days, or they can be frozen for up to 6 weeks.