For the dough:
Combine yeast and milk in the bowl of a mixer fitted with a paddle attachment and mix on low speed.
Slowly add sugar, orange zest, cardamom, vanilla extract, vanilla seeds, eggs, and orange juice. Mix well.
Change the paddle to a dough hook and add salt and flour, one cup at a time, increasing the speed, until the flour is incorporated.
Knead the dough for about 5 minutes, or until it is smooth.
Transfer the dough to a lightly floured silpat, taking care to cover it with plastic wrap.
Refrigerate the dough for 30 minutes.

For folding:
Roll out the dough on a floured surface to a large rectangle of 18″ x 13″ x 1/4″ (35 cm x 30.5 cm x 0.5 cm).
Spread the butter on 2/3 of the dough and fold in 3 (the unbuttered part in the middle, then the last 1/3 on top.
Refrigerate for 30 minutes.
Turn the dough 1/4 turn and roll out again.
Fold in 3 and refrigerate again for 30 minutes.
Repeat the operation 3 times.
After the final turn, refrigerate the dough, wrapped in plastic wrap, for 5 hours or overnight.

Shaping:
Remove the dough from the refrigerator and cut it in half.
Wrap the other half and return it to the refrigerator.

On a floured surface, roll out the dough to a rectangle of 15″ x 6″ (38 cm x 15 cm).
Using a pizza cutter, cut triangles of 3″ (7.5 cm) base.
Place 2 tablespoons of jam, leaving a 1″ (2.5 cm) border at the base edge.
Starting from the base, roll each triangle to form a croissant, stretching and lengthening as you go.
Repeat with the remaining dough.

Place the croissants 2″ (5 cm) apart on baking sheets lined with parchment paper.
Cover them with plastic wrap and let rise for 2 hours in a warm place (72 F/22 C) or until they have doubled in volume.

Baking:
30 minutes before baking, place a water-filled steam pan in the lower third of the oven and preheat the oven to 400 F (200 C).

Brush the croissants with egg wash.
Bake the croissants for 15 to 20 minutes, or until the crust is golden brown.
Remove the croissants from the oven and let them cool on a wire rack.
Once cooled, decorate with classic glaze.

Classic glaze:
Using a whisk, mix powdered sugar and 15% cream in a small bowl until smooth.
Add vanilla extract and mix. Use immediately.