Make the homemade Green Curry Paste in advance, if using.
Boil the tofu (Note 2). Bring a medium saucepan of water to a boil. Slice the tofu into 4 vertical slabs, and gently press down with a towel several times to remove excess water. Chop into ½ to ¾-inch (~1.5 cm) cubes. Add 1 TBSP kosher salt to boiling water (or 1 ½ to 2 tsp sea salt), followed by tofu. When water returns to a boil, set a timer for 2 minutes. Gently drain.
Heat a deep 12-inch sauté pan or medium Dutch oven over medium-high heat. Once hot, add about 4 tablespoons of the coconut milk. Let it bubble and sizzle, and cook until the oil starts to separate from the milk, 1 ½ to 2 minutes. If it doesn’t really separate, don't worry (depends on the brand).
Add curry paste, plus extras if using store-bought curry paste. Cook, stirring frequently, for 3 minutes, until it starts to dry out a bit. The curry paste might sputter so stand back. If the paste sticks, deglaze with a splash of water.
Pour in rest of the coconut milk (1.5 cans for jarred curry paste, 2 full cans for homemade curry paste). Add lime leaves, sugar, and soy sauce, and stir. Bring to a rapid simmer and cook for 3 to 4 minutes, or until it just starts to thicken.
Add the boiled tofu (if using) and gently toss. Add vegetables of choice and broth. Stir to submerge the veg (it's okay if not totally submerged). Partially cover the pan and bring to a rapid simmer, and cook for 6 to 8 minutes, or until the veg is tender but still crisp.
If using baked or fried tofu, add it in. Taste, adding more soy sauce or sugar as needed. If you used lime leaves, remove them; if not, add a squeeze of lime juice. Stir in Thai basil. Flavors will meld and mellow a bit after 15-20 min. Serve over rice and garnish with extra basil and mild red chiles, if using.