Preheat the oven to 350°. Line two 12-cup muffin tins with paper liners. In a medium bowl, toss the carrots with the raisins and pecans. Onto a large sheet of wax paper, sift the flour with the cinnamon, baking powder, baking soda and salt.
In a large bowl, using an electric mixer, beat the canola oil with the sugar at medium-high speed until smooth. Add the eggs, 1 at a time, beating well between additions. Add the dry ingredients and beat at low speed until combined. Using a wooden spoon, stir in the carrot mixture.
Spoon the batter into the cups, filling them three-fourths full. Bake the cupcakes for about 25 minutes, or until the tops spring back when lightly pressed. Let cool in the pans for 10 minutes, then transfer the cupcakes to a wire rack to cool completely.
In a small, deep saucepan, combine the sugar, water and lemon juice. Using a wet pastry brush, wash down the side of the saucepan. Bring to a simmer over moderately high heat and cook without stirring, until the caramel just begins to color around the edges, about 5 minutes. Gently swirl the pan and simmer until the caramel turns a medium amber color, about 2 minutes longer. Remove from the heat. Using a long-handled wooden spoon, stir in the heavy cream. Transfer to a bowl and let cool.
In another bowl, beat the cream cheese at low speed until smooth. Beat in the butter, then beat in the confectioners' sugar and vanilla until smooth.
Spread 1 tablespoon of the cream cheese frosting over each cupcake. Fill a pastry bag fitted with a 1/4-inch star tip with the remaining frosting. Pipe a ring around the top of each cupcake, leaving an empty space in the center. Spoon the caramel into the centers. Transfer the cupcakes to a platter and serve.
The cupcakes can be refrigerated in an airtight container for up to 3 days.
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