Par-Cook the Rice: Bring a medium pot of salted water to a boil.
Stir in the rice and cook until partially done—about 5 minutes for white basmati or 15 minutes for brown. The grains should be soft on the outside but still firm in the center.
Drain well and set aside.
Season with a little more salt and pepper.
Prepare the Saffron Butter: In a small bowl, melt 2 tablespoons (30 ml / 1 fl oz) of the butter (or warm half the olive oil). If using saffron, stir the threads into the warm butter or oil to let them bloom.
Sauté the Fennel: In a large, heavy-bottomed pot with a tight-fitting lid (a non-stick Dutch oven is perfect), melt the remaining 2 tablespoons (30 ml / 1 fl oz) of butter or oil over medium-high heat.
Add the sliced fennel, season with salt and pepper, and cook, stirring, until softened, about 2-3 minutes.
Remove the fennel from the pot and set it aside.
Build the Layers: Turn off the heat.
Pour 1/4 cup (960 ml) of water and the saffron-infused butter/oil into the bottom of the pot.
Peel the potatoes and slice them thinly crosswise.
Arrange the potato slices in a single, even layer, covering the bottom of the pot. Gently spoon half of the par-cooked rice over the potatoes.
Top with the cooked fennel, then cover with the remaining rice, mounding it slightly in the center.
Steam the Rice: Wrap the pot's lid in a clean kitchen towel, ensuring the corners are tied up on top so they don't hang near the flame.
Place the lid tightly on the pot.
Turn the heat to medium-high.
Cook for about 5 minutes, or until you can hear sizzling and spattering.
The Final Cook: Once you hear the sizzle, reduce the heat to the lowest possible setting.
Let the rice steam, completely undisturbed, for 45 minutes. You'll know it's ready when the kitchen smells wonderfully toasty.
Remove the pot from the heat and let it rest, still covered, for 5 minutes.
The Grand Reveal: Carefully remove the lid.
Place a large serving platter over the top of the pot. With confidence, quickly and carefully invert the pot. If you're lucky, the rice will slide out with a perfect, intact potato crust. If some bits stick, simply scrape them out with a spatula and arrange them on top.
Serve immediately!
