Line the base and sides of a springform tin with baking paper.
Break up the cookies and pulse briefly in a food processor until they become fine crumbs.
Cube the butter, place in a microwave-safe bowl, and melt in the microwave for one to two minutes.
Combine the melted butter with the biscuit crumbs and mix until the texture resembles fine breadcrumbs.
Press the mixture evenly into the bottom of the lined springform tin, taking care not to press too firmly.
Chill in the refrigerator for at least one hour or up to overnight.
Ensure the cream cheese is at room temperature.
Slice the lemon and extract the juice.
Beat the cream cheese briefly to soften it.
Add the lemon juice, sugar, and vanilla extract to the cream cheese and beat on low speed until combined and sugar dissolves.
In a separate bowl, add the thickened cream and sift in some matcha powder.
Whisk on medium-low speed until matcha starts to incorporate.
Sift in more matcha in stages, whisking between additions.
Scrape down the sides regularly to mix any lumps.
Increase speed to medium-high and whip until firm peaks form.
Gently fold the matcha whipped cream into the cream cheese mixture until combined.
Spread the cheesecake filling evenly over the chilled base and smooth the surface.
Chill in the refrigerator for at least four hours, preferably overnight.
Remove the cheesecake from the springform tin and smooth edges.
Place a stencil gently on top and dust with matcha powder or dust directly if no stencil.
Slice and serve with matcha tea or matcha latte.