Eritrean Shrimp Thingie

From an old NYT restaurant review (I doubled it):

4 tablespoons olive oil
3 medium red onions, thinly sliced
4 to 6 cloves garlic, minced
5 very ripe and juicy tomatoes, chopped coarsely
Salt and freshly ground black pepper, to taste
1/2 cup finely chopped fresh basil (1 bunch)
15 pitted dates ( 1/2 cup), cut crosswise in thirds
3 tablespoons unsweetened shredded coconut
1/2 cup half-and-half
1 pound medium shrimp (16 to 20), shelled and deveined
2/3 cup grated Parmesan cheese
2 1/2 cups cooked basmati rice
1. In a large, heavy pot, heat olive oil over medium heat. Add onions, and saute until wilted, about 10 minutes. Add garlic, and continue sauteing, stirring frequently to prevent sticking, for 2 minutes longer. Stir in the tomatoes, salt and pepper. Cover, and cook for about 5 minutes. [Uh, more like 25 minutes… -Ed.]
2. Add basil, dates and coconut, and reduce heat to medium-low. Cook, uncovered, stirring occasionally, for 5 more minutes. Add the half-and-half, cover and cook for 3 minutes.
3. Add shrimp to sauce. Cook, covered, until shrimp turns pink, about 5 minutes. Stir in the cheese, and then the rice, and serve immediately.