Lemon Ice Cream Sandwiches with Blueberry Swirl

I seem to have a problem. I can't stop buying cooking magazines! I see them in stores, and just have to buy one. This recipe was on the cover of Gourmet magazine this month, and looked too tasty.
I made these for a group of friends that came over, and they got eaten up pretty quickly! They are a bit of work, but not too bad. You use already made vanilla ice cream. A great way to use ripe local, blueberries.
For lemon ice cream:
2 pt all natural vanilla ice cream (I used Breyers)
1 Tbsp grated lemon zest
2 Tbsp fresh lemon juice

Transfer ice cream to a microwave safe bowl and microwave at 30 percent power in 10 second intervals, stirring until softened.
Stir in lemon juice and zest. Spread ice cream thinly in a 13-by-9 baking dish and freeze while making compote and sandwich layers.

For blueberry compote:
2 cups blueberries (10 oz)
1/4 cup sugar
2 (3-by 2 1/2-inch) strips lemon zest
1 Tbsp fresh lemon juice
2 tsp cornstarch

Cook blueberries, sugar, and zest in a skillet over medium high heat, thoroughly crushing blueberries with a potato masher, until juices are released and sugar has dissolved, about 2 minutes.
Stir together lemon juice and cornstarch, then stir into blueberry mixture. Boil, stirring, 1 minute. (Mixture will thicken.)
Transfer to a bowl and chill until cold, about 1 hour. Discard lemon zest.

Sandwich layers (Make while blueberry compote chills)
1 cup all purpose flour
1/2 tsp caking powder
1/4 tsp baking soda
1/4 tsp salt
1 stick unsalted butter, softened
3/4 cup packed light brown sugar
1 large egg
1/2 tsp pure vanilla extract
Equipment: 2 (8 inch) square baking pans (2 inches deep), a small off-set spatula)

Preheat oven to 375 degrees F with rack in the middle. Butter baking pans and line with foil, leaving a 1-inch overhand on each side, then butter foil.
Whisk together flour, baking powder, baking soda, and salt in a small bowl. Beat together butter and brown sugar in another bowl with an electric mixer a medium-high speed until pale and fluffy, about 3 minutes. Beat in eggs and vanilla. At low speed, add flour mixture in 2 batches, mixing until just combined.

Divide batter between baking pans and spread into thin, even layers with offset spatula. Bake until golden brown but still tender, 10 to 12 minutes. Cool completely in pans, about 30 minutes.

Dollop tablespoons of blueberry compote all over ice cream, then swirl with a spoon. Spoon all of the ice cream over 1 sandwich layer (in pan) and spread evenly using clean offset spatula. Invert second sandwich layer over ice cream, pressing gently to form an even sandwich. Wrap baking pan in plastic wrap and freeze until firm, at least 2 hours.
Transfer sandwich to a cutting board using overhang. Cut into 8 pieces.