1/2 cup raisins
1/4 cup old-fashioned oats
1/2 cup (1 stick) unsalted butter, room temperature
1/2 cup (packed) dark brown sugar
1/2 cup sugar
1 large egg
1 cup (packed) finely grated peeled carrots (from 10 to 12 ounces; grated on small holes of box grater)
1 1/2 cups self-rising flour
1 1/4 teaspoons ground cinnamon
1/2 cup chopped walnuts or pecans- plus additional for garnish (optional)
Preheat oven to 350°F. Line 3 large rimmed baking sheets with parchment. Place raisins and oats in small bowl; add 1/4 cup water. Let soak until water is absorbed, about 15 minutes. Beat butter and both sugars in large bowl until fluffy. Beat in egg, then carrots. Add flour and cinnamon; beat to blend. Stir in raisin-oat mixture and 1/2 cup nuts (batter will be sticky). Drop batter by level tablespoonfuls onto sheets, spacing 1 1/2 to 2 inches apart.
Bake cookies, 1 sheet at a time, until light golden, about 20 minutes (cookies will be soft). Cool on sheets 5 minutes, then transfer to racks and cool completely.
1 cup powdered sugar
6 ounces cream cheese, room temperature
1/4 cup (1/2 stick) unsalted butter, room temperature
2 tablespoons heavy whipping cream
2 teaspoons fresh lemon juice
Beat all ingredients in medium bowl until smooth. Spread icing on cookies.