For the date molasses: Combine the dates and 3 1/2 cups water in a medium saucepan on medium-high heat. Bring to a boil, then reduce the heat to medium-low. Simmer until softened, stirring occasionally and skimming foam every few minutes, about 15 minutes. Once the dates start to soften, use a wooden spoon to mash them. Strain into a clean saucepan through a fine-mesh sieve. Bring to a boil over high heat, stirring occasionally, and cook until slightly thickened, about 5 minutes.
For the pan-roasted apples: Melt the butter in a large skillet over high heat. Add the sugar and cook until starting to brown. Add the apples, lemon juice, cardamom and cinnamon. Cook, tossing constantly, until very well caramelized and soft, about 5 minutes. Add the apple cider; cook until thickened, about 5 minutes. Keep warm.
For the yogurt whipped cream: In a medium bowl, whip the cream, yogurt and vanilla seeds to soft peaks. Chill until ready to serve.
For the French toast: Preheat the oven to 200 degrees F. Set a rack over a baking sheet.
In a baking dish, whisk together the eggs and yolks. Add the half-and-half, vanilla and cardamom; mix until combined.
Add 4 slices of bread to the egg mixture; soak for about 30 seconds on each side. In a large cast-iron skillet over medium heat, heat half of the butter and oil until shimmering. Add the soaked bread and cook until golden brown on both sides, about 3 minutes per side. Transfer the French toast to the rack and keep warm in the oven. Soak and cook the remaining slices of bread, using the remaining butter and oil.
To serve: Place a slice of French toast on a serving plate; top with a spoonful of pan-roasted apples, a drizzle of date molasses, a dollop of yogurt-whipped cream, another slice of French toast, more apples, more yogurt and a final drizzle of date molasses. Serve immediately.