How to Make It
Preheat oven to 350°F. Lightly grease the bottom and sides of an 8-inch springform pan with oil. Line bottom of greased pan with parchment paper, and lightly grease parchment; set pan aside.
Whisk together flours, baking powder, and baking soda in a medium bowl.
In the bowl of a stand mixer fitted with the whisk attachment, or in a large bowl with an electric mixer, beat 1/2 cup sugar and eggs on medium-high until pale yellow and slightly thickened, about 3 minutes. Beat in 1/2 cup oil, 1 teaspoon lime zest, 31/2 tablespoons lime juice, and vanilla. With mixer running on low speed, gradually add flour mixture until just incorporated.
Pour batter into prepared pan. Bake in preheated oven until top is dark golden brown and a toothpick inserted in center comes out with crumbs attached, 40 to 45 minutes. Cool in pan on a wire rack 10 minutes. Remove outer ring, and invert cake onto wire rack. Remove bottom of pan and parchment; cool cake completely, about 1 hour.
Stir together strawberries, remaining 1 teaspoon zest, and remaining 1 teaspoon sugar in a medium bowl. Let stand at room temperature 30 minutes to 1 hour.
Whisk together yogurt, cream, honey, and remaining 1 teaspoon lime juice until incorporated.
Top each cake slice with large spoonfuls of yogurt mixture and strawberries.