Prepare all the ingredients (remember that the eggs, yogurt, and butter must be at room temperature so take them out of the fridge about 1-2 hours before making the cake).
Prepare a 9×5 inch loaf pan (23×13 cm) or 10×4.5 inch (25.5×11.5cm) by buttering it and lining it with parchment paper.
Preheat the oven to 350 °F / 180 °C / Gas Mark 4, no fan.
In a big mixing bowl cream the cut into cubes butter with sugar, which means: beat the butter with sugar using a paddle attachment for about 3 minutes over low speed or until the mixture is light and fluffy.
Add the eggs to the bowl and beat for a couple of minutes until they are combined with the butter-sugar mixture.
In another medium bowl stir the flour with baking powder and salt.
Add 1/2 of the flour mixture to the batter bowl, mix until almost combined (with a whisk or with a mixer at low speed).
Add 1/2 of the yogurt and mix gently until almost combined.
Add the remaining 1/2 of the flour mixture and mix until almost combined.
Add the remaining 1/2 of the yogurt and the vanilla extract, mix until combined.
Wash the rhubarb, pat it dry with paper towels, cut it into 1/2-inch (1cm) pieces (there is no need to peel the rhubarb), toss with 2 tablespoons of flour.
Using a silicone spatula, fold 3/4 of the rhubarb into the batter.
Transfer the batter into the baking pan, even out the surface with the spatula.
Place the remaining 1/4 of the rhubarb on top of the batter, press it slightly in.
Move the baking rack to the second lowest position and bake the cake for about 60-70 minutes or until a wooden skewer (cake tester) inserted in the middle of the cake comes out clean. After about 55 minutes of the baking time check if the cake is not browning too much. If so, cover it loosely with a piece of aluminum foil.
Take the cake out of the oven and leave it for 10 minutes in the baking pan. Then take the cake out of the pan and leave on a cooling rack for a minimum of 20-30 minutes until cooled down (best would be if the cake is completely cooled down, but it's ok if just slightly warm).
Sprinkle the cake with powdered sugar and slice it into servings.
Enjoy!