Make cookies: In a medium bowl, whisk together flour, cinnamon, baking soda, and salt. In a small bowl, stir together coconut oil, honey, water, and vanilla. Add honey mixture dry ingredients and stir until fully combined. Turn the dough out onto a counter and gently bring it together into a ball. Wrap in plastic wrap and refrigerate for 30 minutes.
Preheat oven to 350°F. Place chilled dough on a piece of waxed paper and top with a second piece of waxed paper. Roll dough into a ¼-inch-thick rectangle and cut into 3 ½-inch square cookies. Gather and reroll the dough scraps and cut 3 more cookies. (You may need to chill the dough before rerolling if your kitchen is warm.) Carefully arrange the cookies on a parchment-lined baking sheet and bake until lightly browned and starting to turn crisp, 12 to 15 minutes. Let cookies cool on baking sheet on a wire rack for a few minutes, then transfer to a rack to cool completely.
Make cake: Line a 9-by-5-inch loaf pan with plastic wrap, leaving a 3-inch overhang on all sides. Reserve 8 oz. of the smallest, most attractive strawberries; cover and refrigerate. Chop remaining strawberries and place in a small bowl. Add 1 tablespoon honey and gently mash.
In a medium bowl, using an electric mixer, beat yogurt with remaining 10 tablespoons honey and vanilla until well combined. Add cream and beat until thick, about 2 minutes.
Spread about 1 ¾ cups of yogurt cream evenly in bottom of prepared loaf pan, making sure there are no gaps. Arrange 2 cookies on top—they should almost cover the yogurt with a border around all sides. Press gently on the cookies to eliminate any gaps. Carefully arrange half of strawberry mixture on top of cookies, leaving yogurt-cream border around edges. Spread about 1 ¾ cups of yogurt cream evenly on top of strawberry mixture, gently pressing down to fill in any gaps and taking care not to disturb strawberry layer. Top with a second cookie layer, followed by a second strawberry layer. Carefully spread remaining yogurt cream over the strawberries, gently pressing down. Top with a final cookie layer, gently pressing cookies into yogurt cream. Wrap the overhanging plastic wrap over cake, then wrap the entire loaf pan tightly in another layer of plastic wrap. Freeze overnight. (The icebox cake can be made up to 2 days in advance.)
When ready to serve, thinly slice reserved strawberries. Remove icebox cake from freezer. Remove outer layer of plastic wrap and lift overhanging plastic from top of cake. Invert cake onto a platter and carefully remove loaf pan and plastic wrap. Top with sliced strawberries, slice cake, and serve.