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1
Generously grease a loaf pan (don't skimp; you can also line it with a parchment sling if that makes you more comfortable) and heat the oven to 350u00b0 F with a rack in the center.
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2
Mix the rhubarb with 1/4 cup of sugar and place in a medium skillet or sauce pan. Turn the heat to medium and cook, stirring often, until the sugar and rhubarb juices melt into a syrup and the rhubarb chunks are fork-tender, about 5 minutes. Do not over-cook the rhubarb (it shouldn't be mushy, watery, stewy, or soupy) or it will disappear into the cake. Set aside to cool.
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3
In the bowl of a stand mixer fitted with a paddle attachment, mix the remaining 1 1/4 cups sugar with the lemon zest until moist and fragrant. Add the butter and cream it with the lemon-sugar until fluffy and pale, 3 to 5 minutes. Add the eggs one at a time, mixing well after each addition and scraping down the sides of the bowl. Add the vanilla and 1/3 cup of the Greek yogurt and mix until combined.
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4
Whisk the flour, matcha, baking powder, and salt together in a separate bowl. Add to the wet ingredients and mix until the dry ingredients have just disappeared. Fold in the rhubarb with a spatula. Transfer to the greased pan. Bake for 55 to 70 minutes, until a cake tester inserted into the middle of the loaf comes out clean. Allow to cool before turning it out of the pan.
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5
Meanwhile, make the glaze: Whisk the remaining 1/3 cup Greek yogurt with the confectioners' sugar, the lemon juice, a pinch of salt, and 1/2 teaspoon water until smooth. Drizzle over the cake and allow to set for about 30 minutes before slicing and serving.
