To make the jam, cut the rhubarb into a 1-inch dice and place in a medium saucepan. Hull the strawberries and slice into a bowl. Using a potato masher or fork, roughly mash the berries until chunky. Throw into the pot with the rhubarb, along with the lemon juice, vanilla and salt. Cover and cook over moderate heat for 5 minutes. In a small bowl, whisk together the sugar and cornstarch and stir into the saucepan. Bring to a boil; cook and stir until thickened, about 2 minutes. Remove from the heat and set aside to cool completely.
Preheat oven to 425 degrees F. Grease a standard muffin pan with melted butter or non-stick cooking spray, set aside.
In a large bowl, whisk together the flour, baking powder, baking soda and salt.
In a separate bowl, cream together the butter, oil, granulated sugar and brown sugar until light and fluffy, about 3 minutes. Stir in the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract until well-combined.
Add the dry ingredients, alternately with the buttermilk, starting and ending with the dry ingredients. Make sure to mix until just combined after each addition. Do not over mix at this point. Spoon the batter into the prepared pan, filling the pans nearly full. Bake until pale golden brown and a toothpick inserted in the middle comes out clean, about 15 to 18 minutes. Remove from the oven and let cool for about 5 minutes before transferring to a wire rack to cool completely.
Pour the melted butter into a small dish. In a separate bowl, combine the sugar and cinnamon. Brush each muffin with the melted butter and then roll around in the cinnamon sugar mixture. Place the coated doughnuts onto a small baking sheet lined with parchment paper.
Transfer the cooled jam to a disposable piping bag, fitted with a plain circle tip. Using a sharp pairing knife, cut out a small hole on top of each doughnut. Pipe out about a tablespoon of filling into each. You'll have leftover jam but you can keep it in an airtight container in the fridge for up to 2 weeks. Serve the doughnuts immediately, or wrap in plastic wrap and keep at room temperature for up to 2 days. Enjoy!