For the peas: Heat the canola oil in a medium saucepan over medium-high heat until it shimmers. Add the onion halves to the pan cut side down and cook, undisturbed, until the bottoms are caramelized to a very dark brown, about 3 minutes. Add the vegetable stock, vinegar, bay leaf, thyme, and peas and bring to a boil. Reduce the heat to low and simmer until the peas are tender, about 25 minutes.
Drain the peas, reserving ¼ cup of the cooking liquid, and discard the bay leaf, thyme, and onion. Transfer the peas to a medium saucepan and season lightly with salt and white pepper. Add the reserved cooking liquid, cover, and set aside.
For the succotash: Heat the butter in a large skillet over medium-high heat until foamy. Add the onion and garlic and cook, stirring frequently, until the onion is translucent, about 4 minutes. Add the bell peppers and cook, stirring frequently, until they soften, about 5 minutes.
Add the hominy, the crowder peas and their liquid, and the vegetable stock to the skillet and bring to a simmer. Cook, stirring occasionally, until the stock has reduced by half, about 3 minutes. Add the cream and cook, stirring occasionally, until the liquid has reduced by half and slightly thickened, 1 to 2 minutes.
Season the succotash liberally with salt and white pepper and stir in the lemon juice. Fold in the cheese and fines herbes and serve.
For the hominy: Combine the corn, 3 cups of the water, and the culinary lime in a large nonreactive saucepan and bring to a boil over high heat, stirring occasionally. Reduce the heat to low and simmer, stirring occasionally, until the hulls of the kernels begin to soften, about 35 minutes.
Drain the corn in a colander and rinse very well under cold running water. Transfer to a large nonreactive pot, add the remaining 8 cups water and 1½ teaspoons of the salt, and bring to a boil over high heat. Reduce the heat to low and simmer, stirring occasionally, until the kernels are soft but not splitting, about 1 hour. Drain the corn, reserving 4 cups of the cooking liquid.
Combine the corn, reserved cooking liquid, chicken stock, and remaining 2 tablespoons salt in a large nonreactive saucepan and bring to a boil over high heat. Reduce the heat to low, cover, and cook, stirring often, until the kernels are completely soft and splitting, about 45 minutes. Drain the corn, spread it out on a rimmed baking sheet, and cool to room temperature.
Transfer the cooled hominy to a container, cover, and refrigerate for up to 3 days.
For the fines herbes: Combine all the herbs in a small bowl and mix well. Line a container with paper towels, transfer the herbs to it, cover, and refrigerate until ready to use. Tightly covered, the herbs will keep for up to 1 day in the refrigerator.
