For the French toast: Preheat the oven to 275 degrees F.
Cut each slice of bread lengthwise into thirds (18 pieces total). Transfer to a baking rack set over a baking sheet and bake for 30 minutes to dry out. Remove from the oven and let sit for another 30 minutes before making the French toast.
Meanwhile, make the ganache: Whisk the heavy cream and almond butter together in a small saucepan, and bring to a simmer over low heat, stirring occasionally¿the mixture doesn't have to be completely smooth. Remove from the heat, cover, and let steep for 10 minutes.
Put the white chocolate in a heatproof bowl. (If the cream has cooled off significantly, reheat it nearly to a simmer.) Strain the hot cream over the chocolate through a fine strainer, add the orange zest, and let sit for 1 minute. Whisk until smooth. Keep warm.
Continue with the French toast: Whisk together the 1 cup sugar, cinnamon and star anise in a shallow baking dish.
In a bowl, whisk together the eggs, egg yolks, 2 tablespoons sugar, half-and-half and vanilla extract until very smooth. Transfer to a second shallow baking dish.
Working in batches to avoid crowding the pan later on, soak the bread until saturated, turning a few times, about 3 minutes total.
In a large nonstick skillet over medium heat, heat half of the oil and half of the butter until melted and shimmering. In batches, add the soaked bread and cook, turning, until golden brown on all sides, about 30 seconds per side. Immediately remove from the pan, toss in the spiced sugar, and transfer to a platter. Repeat with the remaining oil, butter and bread.
Serve the churros warm with the ganache for dipping.