In a large bowl, whisk together: 1 seeded finely minced hot finger pepper, 8 cloves finely minced garlic, 1 tablespoon finely grated fresh ginger, 1 cup full-fat yogurt, 1 tablespoon Kashmiri chili powder, 1 teaspoon ground turmeric, 1 ½ tablespoons garam masala, 1 tablespoon coarse salt, and the juice of 1 lemon (about 2–3 tablespoons). Taste and adjust only if needed. Set the marinade aside.
Remove skin from the chicken breasts, thighs, and drums (if present). On each piece, make 2 to 3 shallow slashes about 1/4" to 1/2" deep. Place the chicken pieces into the marinade and mix thoroughly so each piece is well coated. Cover and refrigerate for at least 4 hours and up to 24 hours.
Heat ½ cup avocado oil in a large 10-quart Dutch oven over medium heat. Add the 2 peeled and thinly julienne sliced red onions and fry, stirring occasionally, until brown and crispy, about 15–18 minutes. Use a slotted spoon to transfer the fried onions to a paper towel–lined plate to drain. Leave the oil in the pot.
Rinse 3 cups basmati rice in a fine-mesh strainer under cold running water until the water runs clear. Keep the rice in the strainer and place it briefly in a large bowl of cold water, then drain and set aside.
In a separate large 6-quart pot, heat 2 tablespoons ghee over medium-high heat. Add 1 bay leaf, 1 star anise, 5 cloves, 5 green cardamom pods, 2 black cardamom pods, 1 cinnamon stick, 1 teaspoon cumin seeds, and 1/4 teaspoon fennel seeds. Sauté for 1–2 minutes until fragrant.
Pour 1 gallon of water into the spice pot and bring to a rolling boil over high heat. Season the boiling water with coarse salt to taste. Add the rinsed rice and cook, uncovered, for 5–7 minutes until the rice is about 75% cooked (al dente). Drain the rice in a colander and spread it on a sheet tray to cool briefly.
Return to the 10-quart Dutch oven with the oil remaining from frying the onions and heat over medium-high. Add the marinated chicken pieces and the 2 peeled russet potatoes cut in half and thickly sliced; stir to submerge and mix the potatoes among the chicken. Cook for 5–6 minutes.
Flip the chicken pieces and continue cooking another 5–6 minutes so the exterior is lightly seared and the potatoes begin to soften.
Add 2/3 of the fried onions, 3 tablespoons minced fresh mint, 3 tablespoons minced fresh cilantro, and 1 ½ cups medium-diced fresh tomatoes to the pot. Stir gently to combine and cook for 3–4 minutes.
Flatten the chicken, potatoes, and tomato mixture evenly in the pot. Spoon half of the cooked rice over the mixture (do not pack it down). Divide the ¼ cup minced fresh mint and the ¼ cup minced fresh cilantro into two equal portions; sprinkle one portion of each over the rice. Top this layer with half of the remaining fried onions and season lightly with coarse salt to taste.
Repeat the layering: add the remaining rice, then the second portion of the divided ¼ cup minced mint and ¼ cup minced cilantro, and finish with the rest of the fried onions. Drizzle the remaining 4 tablespoons ghee evenly over the top.
In a small bowl, warm 3 tablespoons heated whole milk, add 12–15 saffron threads, and let steep 2–3 minutes until the milk is colored. Strain the saffron and pour the saffron milk in a circular motion over the top of the rice.
Cover the pot tightly first with foil and then with the lid. Cook over very low heat (dum) for 30–35 minutes, until the chicken is fully cooked and the potatoes are tender.
Remove the pot from heat. Carefully uncover, gently fluff the top layer of rice to reveal the chicken and potatoes, and plate portions of chicken biryani. Garnish with any remaining fried onions and any reserved minced cilantro and mint.