In a large mixing bowl, combine cold heavy cream, powdered sugar, and vanilla. Beat with electric mixer on medium-high until stiff peaks form (about 3-5 minutes). Keep cold.
Trim crusts off bread slices if desired. Wash and dry strawberries thoroughly. Cut 4-6 strawberries in half lengthwise for even slices.
Place bread slices on a board. Spread a thick layer of whipped cream (about ¼-inch) on one side of each slice. Make it higher in the center for stability.
On two slices, place strawberries cut-side down in an X or diagonal pattern across the center. Fill gaps with more cream to cover fruit completely.
Top with remaining bread slices (cream-side down). Press gently to adhere. Wrap each sandwich tightly in plastic wrap.
Refrigerate 1 hour or overnight to set cream and make slicing easier.
Unwrap, mark diagonal line with marker for fruit cross-section. Slice in half with serrated knife. Serve cold.