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Preheat the oven to 350°F. Prepare an 8" square pan with a parchment sling or reusable silicone liner, then lightly grease the sides of the pan. Alternatively, line a 9" cake pan with a round piece of parchment or round reusable liner and lightly grease the sides.
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To make the strawberry topping: In a small bowl, stir together the diced strawberries and sugar. Transfer the mixture to a strainer placed over a bowl. Let the strawberries drain for 45 to 60 minutes, tossing occasionally; set the strawberries aside and reserve the juice. (You should have about a scant 1/4 cup of juice.)
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To make the matcha filling: In a small bowl, combine the sugar and matcha. Set aside.
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To make the crumbs: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a medium bowl, whisk together the flour, sugars, and salt. Add the butter and vanilla; toss to combine. Using a bowl scraper, fork, or your fingers, work in the butter until crumbs form and no dry spots remain. The crumbs should be irregular, ranging in size from a pea to walnut. Set aside.
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To make the cake: In a large bowl or bowl of a stand mixer, combine the flour, sugar, baking powder, salt, and baking soda. Add the butter and mix at low speed using an electric hand mixer or the flat beater on a stand mixer until the mixture looks sandy, about 1 to 2 minutes. (This mixing method is called reverse creaming and is also known as the paste method.)
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Beat in the vanilla and eggs, then mix until no dry spots of flour remain. Stop the mixer and scrape the bowl and beater(s) as needed; the mixture will be thick.
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Add the yogurt or sour cream all at once before starting to mix. Continue to stir until the batter is smooth. Stop to scrape the bowl and then mix again at low speed for 1 minute; this final mix is key to ensuring the best texture so don't skip it.
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To assemble and bake the cake: Transfer half the batter (about 1 1/2 cups, 420g) into the prepared pan, spreading it all the way to the edges. (A small offset spatula is a helpful tool here.)
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Sprinkle the matcha filling evenly across the batter.
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Transfer the remaining batter to the pan by dolloping portions over the filling. Use a spatula to smooth it out into an even layer. It’s OK if a little bit of the filling gets mixed into the top layer of batter.
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Sprinkle the diced strawberries (from step 2) evenly over the top of the batter, followed by the crumbs. Gently press the crumbs to adhere.
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Bake the strawberry coffee cake for about 48 to 52 minutes, until it's set in the middle and the crumbs are lightly browned. When the cake is done, a toothpick or paring knife inserted into the center should come out mostly clean.
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Remove the coffee cake from the oven and allow it to cool in the pan for 30 minutes. While the coffee cake is cooling, prepare one of the glazes.
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To make the glaze: In a small bowl, stir together all the ingredients for your glaze of choice (choose one: strawberry or matcha) until smooth, starting with smaller amount of water. Add additional water as needed until the glaze is the consistency of molasses.
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Remove the strawberry coffee cake from the pan using the overhanging edges of parchment as handles to gently lift it out. Place the coffee cake (still on the parchment) on a wire rack.
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Drizzle the glaze over the coffee cake, or finish by dusting with non-melting sugar or confectioners’ sugar.
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Storage information: Store the strawberry coffee cake, well wrapped, at room temperature for several days; freeze for longer storage.
