1. To make the truffies: Combine the white chocolate, butter, cream, and salt in a double boiler or in a heatproof bowl set over a saucepan of gently simmering water and heat, stirring occasionally, until the chocolate and butter are completely melted and smooth. Whisk in the matcha until fully incorporated. Transfer the ganache to a shallow dish and refrigerate, uncovered, until firm.
2. When the ganache is almost set, make the chocolate cakes: Preheat the oven to 425°F. Generously butter and flour eight 4-ounce ramekins and set aside.
3. Melt the butter and chocolate in a double boiler or in a heatproof bowl set over a saucepan of gently simmering water, stirring occasionally, until completely melted and smooth. Remove from the heat.
4. Put the yolks, salt, and half the sugar in a large mixing bowl and whisk just until blended. Add the melted chocolate mixture, whisk well, and set aside.
5. Put the egg whites in the bowl of an electric mixer fitted with the whisk attachment and whisk at medium-high speed until frothy. With the machine running, slowly add the remaining sugar and continue whisking until medium peaks form. (When you lift the whisk from the mixture, a peak will form and the very tip of the peak will fall back down.) Whisk in the cornstarch until incorporated.
6. Whisk half the whites into the yolk mixture until fully incorporated, then gently fold in the remaining whites. Divide the batter evenly among the ramekins.
7. Use a 1-inch diameter ice cream scoop or a measuring spoon to scoop the white chocolate mixture into eight 1-inch balls. Press a ball into the center of each ramekin and use the back of a spoon to smooth the batter over the truffle until it is covered.
8. Bake until the cakes are a dark chocolatey brown and dry to the touch, about 7 minutes; they should have risen about ½ inch above the rim of the ramekins. Cool for 1 minute in the ramekins, then invert onto serving plates and serve.