Preheat oven to 350ºF. Line a 9x13" metal baking pan with parchment or grease well. In the large bowl of a standing mixer, beat butter and sugar until light and fluffy, about 3 minutes. Beat in egg, then vanilla.
In a separate bowl, whisk together flour, baking soda and salt. With the mixer speed on low, beat in half of flour mixture, followed by yogurt, then remaining flour mixture. Don't overmix - a few flourly streaks are fine.
Remove bowl from standing mixer, and fold in rhubarb and strawberries. It'll be a very stiff batter (that's normal - the fruit releases a log of juices). Spread into prepared baking pan using an oiled spatula or even oiled hands. Again, it's stiffer than typical cake batter and won't just pour in. Normal!
Make Streusel Topping
In a small bowl, combine remaining 1/4 cup butter with brown sugar and cinnamon. Sprinkle over top of cake. Bake for 30 to 40 minutes or until center is set and springs back when lightly touched. It should be 190ºF internal temperature in the middle.Cool in pan set on top of wire rack. Serve warm or at room temperature.
Notes
If you use anything other than an aluminum (metal) baking pan, it can increase the baking time significantly.
The cake batter looks very thick and stiff, and that's normal. It's because the fruit will add a ton of moisture to the batter. Don't be tempted to add more yogurt or any other liquid.
A cooking thermometer is the easiest and most accurate way to tell doneness.