Blend tomatoes, roasted peppers, broth, shallot, garlic, basil, salt and pepper until smooth. Pour into a 5-quart slow cooker, cover and cook on low for 3 to 4 hours.
Turn to high and stir in shredded kale. Cover for 15 minutes until the greens begin to soften.
Fold in uncooked refrigerated tortellini so each piece is coated with hot sauce. Cover and cook for 20 to 25 minutes, gently stirring after 10 minutes, until the pasta is tender at the pinched seams.
Switch off and fold in goat cheese until it melts into a smooth creamy sauce. Let stand for 3 minutes so the filling and sauce settle.
Divide among six bowls and serve promptly, keeping the tortellini whole rather than stirring repeatedly after it has softened.