In a large saucepan, bring the cream and caraway seeds to a boil over medium-high heat. Cook, stirring occasionally, until the mixture is reduced by about half, 8 to 10 minutes. If desired, strain the cream and discard the caraway seeds.
Heat a large skillet over medium-high heat. Add half of the cabbage and 1/4 cup water; season with salt and pepper. Cook, tossing with tongs, until the cabbage is crisp-tender and the water has evaporated, about 5 minutes. Transfer to a serving bowl. Repeat with the remaining cabbage.
Toss the cooked cabbage with the cream mixture. Sprinkle with the parsley.