Preheat oven to 300 degrees. Remove false bottom of springform pan, cut a circle out of parchment approx. 2″ wider than the bottom. Place paper over the bottom, then replace ring so paper lines pan and slightly protrudes around edges. Tighten springform ring, pulling paper to prevent wrinkles.
In a small bowl, mix cookie crumbs and butter to moisten. Gently press into bottom of pan. Chill until ready to use.
In a small bowl, combine 1 c sugar with cornstarch; reserve. In large bowl, whisk together yogurt, eggs, lemon zest and 1?2 c sour cream. With a paring knife, slit vanilla bean in half and scrape inside with edge of blade, adding paste to yogurt mixture. Whisk in sugar/cornstarch and combine well.
Gently pour yogurt mixture into springform pan. Place on a rimmed sheet pan and bake 45 min; rotate and bake 30 min more until center is just set; center should jiggle but should not be runny when you tap on pan.
Remove cake from the oven and cool 30 min. Whisk 1 c of sour cream with remaining 1/4 c sugar.
For icing and decorating your cheesecake, gather sweetened sour cream, lemon curd, zippable plastic bag, scissors, bamboo skewer and spatula to spread icing. Dollop sweetened sour cream over cake. Smooth to cover evenly.
Place lemon curd in a small, zipped plastic bag. Snip bag corner to create a simple piping bag. Pipe thin stripes of curd on top of the sour cream, evenly spaced.
To create a basket weave design, bring blunt end of bamboo skewer downward in opposite direction of stripes, dragging the skewer through the sour cream without scraping the cake. Repeat back and forth, making evenly spaced lines until entire design is complete.
Bake 15 min. Remove and refrigerate on rimmed baking pan overnight (may release liquid while cooling).
To serve, run a knife along inside of pan. Slowly release and remove ring. Use a wide, flat spatula to slide cake onto platter.
* Use whole-milk, full-fat Greek yogurt; not low-fat or non-fat.