Whisk together 2 large eggs and 2 yolks in a bowl until well combined. In a saucepan, combine orange juice, cream, sugar, and salt. Stir until warm, then gradually pour into eggs while whisking.

Return mixture to stove and cook, stirring constantly, until thickened (about 5 minutes). Strain and stir in vanilla. Allow to cool.

Preheat oven to 200°F and place a baking sheet inside. Melt butter in a skillet over medium heat.

Dip slices of bread into custard mixture, coat both sides, and place in skillet. Cook each side until golden brown (about 3 minutes each).

Transfer cooked slices to baking sheet in oven to keep warm. Repeat for remaining pieces.

Dust with powdered sugar, sprinkle with orange zest, add orange segments, and drizzle with syrup before serving.