Semifreddo, which means "half-cold" in Italian, is a semifrozen cross between ice cream and mousse.
In a medium saucepan, combine 3 cups of the strawberries, ¼ cup of the sugar, 4 sprigs thyme, the vanilla bean and seeds, and salt. Cook the mixture over medium heat just until the strawberries begin to soften slightly, about 4 minutes. Remove form the heat and let cool to room temperature. Remove the thyme sprigs and vanilla bean and process the strawberry mixture in a food processor until somewhat smooth. Stir in chopped thyme.
In a large bowl over a pot of very barely simmering water, whisk together the egg yolks and ¼ cup of the sugar. Make sure the bottom of the bowl isn't touching the water. Using an electric mixer or with a large whisk, still with the bowl held over the simmering water, beat the yolk mixture until pale yellow, thick, and doubled in volume, 3 to 5 minutes. Remove from the heat and beat the yolk mixture another minute, then fold in the strawberry mixture.
Beat the cream to medium-stiff peaks. Fold the cream into the strawberry mixture. Pour the strawberry mixture into a loaf pan lined with plastic wrap. Fold the plastic wrap over the top to cover completely. Freeze until firm, at least 6 hours.
When ready to serve, toss the remaining 1 cup of sliced strawberries with the remaining tablespoon of sugar. Let the semifreddo stand at room temperature for 5 to 10 minutes. Unwrap and invert the semifreddo onto a serving plate, remove the plastic, and top with the strawberries. Cut the semifreddo into slices and serve. Store leftovers well wrapped in the freezer.