Preheat your oven to 350°F.
In a large bowl, toss in your rhubarb, strawberries and lemon juice.
Toss two tablespoons of butter on a 10–12-inch ovenproof skillet and heat the skillet over medium heat. Pour your ¼ cup of brown sugar into the mixture and stir them together after the butter melts.
After the mixture has melted and starts to bubble, leave the pan aside and let it cool for a short 5 minutes. After the 5 minutes have passed, coat the pan in nonstick cooking spray and add your rhubarb + strawberry mixture into the pan. Stir everything together so that your ingredients are well coated.
Bring out two medium-sized bowls, an electric mixer, and a whisk. Put your flour, baking soda, baking powder and salt in one bowl and whisk them together.
In your second bowl, add the rest of your brown sugar and butter, and canola oil, and mix them with an electric mixer for about a minute.
While mixing, beat in eggs, one at a time. Then, add yogurt, vanilla, and nutmeg and beat everything until smooth. Get your flour mixture and add it in. Slowly mix everything together until your cake batter is smooth.
Spread the batter over the skillet. Make sure your strawberry and rhubarb are laid out evenly across the skillet. They should be incorporated into the batter very easily.
Bake the cake in your preheated oven for 30 minutes. After the time has passed, use the toothpick test to determine if the cake is done. If not, bake for an additional 5-10 minutes. The cake should have a golden-brown top once ready.
Once the cake is done, put the skillet on a wire rack until it cools off. Once cooled, invert the cake onto a serving platter (serve it upside-down).
Cut slices and serve when ready.