Cut soda bread into ½-inch slices, discarding ends. In a large bowl, whisk together eggs, cream, sugar, vanilla, and salt. Dip each slice into egg mixture, saturating well.
In a large skillet, melt 2 tablespoons butter over medium heat. Working in batches, place slices in the skillet and cook until golden brown on both sides, about 4 minutes per side. Add more butter as needed. Serve warm with clotted cream or whipped cream and preserves on the side.