Medium-grain brown rice has a toothsome texture and nutty flavor that complement creamy, earthy goat cheese in these elegant cakes. Serve over salad greens as a main course.
- Bring rice and water to a boil in a medium saucepan. Reduce heat to low, cover, and simmer at the lowest bubble until the water is absorbed and the rice is tender, 30 to 50 minutes (see Test Kitchen Note). Remove from the heat and let stand, covered, for 10 minutes.
- Meanwhile, heat 2 teaspoons oil in a large skillet over medium heat. Add shallots; cook, stirring often, until soft, 2 to 3 minutes. Add carrots, reduce the heat to low and cook, stirring often, until softened and the shallots are lightly browned, about 4 minutes. Remove from the heat.
- Preheat oven to 400°F.
- Transfer the cooked vegetables and rice to a large food processor. Add pecans, goat cheese, egg white, thyme, salt and pepper. Pulse until well blended but still a little coarse. Scrape into a large bowl. With wet hands, form the mixture into six 3-inch patties (about 1/2 cup each).
- Heat the remaining 2 teaspoons oil in a large nonstick skillet over medium heat. Add the patties and cook until well browned, 3 to 4 minutes per side. Transfer to a baking sheet and bake until an instant-read thermometer inserted into the middle registers at least 160°F, 10 to 15 minutes.