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1
Preheat the oven to 350F.
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2
Line a standard 12-cup muffin tin and a 6-cup tin with paper liners.
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3
Sift the flour, cinnamon, baking soda, salt, nutmeg, and cloves together into a medium bowl.
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4
Set aside.
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5
Put 8 tablespoons (1 stick) butter, the granulated sugar, and 1/2 cup brown sugar in the bowl of an electric mixer fitted with the paddle attachment.
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6
Cream on medium speed until smooth, about 3 minutes.
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7
Mix in the eggs, 1 at a time.
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8
On low speed, mix in the applesauce and then the flour mixture.
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9
Stir in the nuts by hand.
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10
Divide the batter among the muffin cups, filling each about three-quarters full.
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11
Bake until a tester inserted in the centers comes out clean, 18 to 20 minutes.
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12
Let cool completely in the tins on a wire rack.
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13
Meanwhile, in the clean bowl of the electric mixer, mix the cream cheese with the remaining 8 tablespoons (1 stick) butter and 1 cup brown sugar on medium speed until smooth.
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14
Spread the cream cheese frosting on the muffins.
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15
The muffins can be refrigerated in airtight containers up to 2 days.
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16
Bring the apples and cider to a boil in a medium saucepan over medium-high heat.
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17
Cover the pan; reduce heat.
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18
Simmer until the apples are very soft, about 12 minutes.
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19
Stir in the sugar and salt.
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20
Cook (uncovered) over medium-low heat until the apples have broken down and most of the liquid is evaporated, about 15 minutes.
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21
Let cool slightly.
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22
Puree in a food processor until smooth.
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23
Add more sugar, if desired.
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24
Store in an airtight container up to 2 days.
