In a large bowl, with mixer on medium speed, beat powdered sugar and butter for 2-3 minutes or until fluffy. Add egg white and vanilla; beat for 1-2 minutes or until incorporated. Add flour and salt; beat on low speed for 1-2 minutes or just until incorporated. Add lemon zest and poppyseeds; beat 30 seconds or just until incorporated.
Transfer dough to work surface dusted with flfl our; form dough into 14 x 2-inch log and wrap with plastic wrap. Refrigerate dough at least 1 hour or up to 1 day.
Preheat oven to 350°F. Line 2 half sheet trays with parchment paper. Slice dough on a slight bias into 20 (½-inch thick) slices; place 2 inches apart on prepared trays.
Bake shortbread crostini for 18-20 minutes or until the edges are lightly browned and feel firm. Cool crostini on trays 30 minutes
Heat 1 cup strawberries, rhubarb, sugar, lemon zest and lemon juice in a medium saucepan to a boil. Reduce heat to low and simmer for 10 minutes. Add remaining 1 cup strawberries and simmer for 5 minutes. Cool 30 minutes.
In a medium bowl, with mixer on medium speed, beat chèvre, cream cheese and honey for 2 minutes. Increase speed to high and beat for 30 seconds or until light and fluffy.
Spread each shortbread crostini with 1 teaspoon whipped chèvre; spoon 1½ teaspoons strawberry-rhubarb compote over chèvre. Garnish with chopped basil and/or lemon zest.