Caribbean Pepper Pot with Chicken and Shrimp

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1 tablespoon vegetable oil

4 skinless, bone-in chicken thighs (about 1 pound)

1 1/2 teaspoons kosher salt, plus more to season chicken

Freshly ground black pepper

1 medium onion, halved and sliced

3 cloves garlic, smashed

1 teaspoon ground allspice

1/2 cup canned chopped tomatoes

4 cups chicken broth, low-sodium canned or homemade

1 bunch kale (about 1/2 pound), stemmed, leaves chopped

2 thick sweet potatoes (about 1 pound), halved lengthwise and sliced into 3/4-inch half-moons

4 ounces fresh okra, trimmed, halved lengthwise

2 bay leaves

1 Scotch bonnet chile, pierced (if you like it very spicy, mince it) *see Cook's Note

1/2 heaping teaspoon dried thyme

1/3 cup light coconut milk

8 ounces medium shrimp, peeled