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Preheat the oven to 400°F. Spread the pecans on a rimmed baking sheet, and bake until golden, shaking the pan occasionally, 6 to 8 minutes. Transfer the pecans to a work surface to cool, then finely chop them.
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Peel the carrots and grate them on the large holes of a box grater (you should have about 1 1/4 cups or 123g of grated carrot).
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In a large bowl, whisk together the flour, baking powder, salt, cinnamon, and ginger.
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Using a bowl scraper, pastry blender, or your fingertips, work the butter into the dry ingredients just until the mixture is unevenly crumbly; it's OK for some larger chunks of butter to remain unincorporated.
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Add the pecans, carrots, and cinnamon bits to the bowl. Stir gently until incorporated.
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In a medium bowl or liquid measuring cup, whisk together the egg, cream, and sugar until well-combined.
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Make a well in the center of the dry ingredients and add the egg mixture. Use a flexible spatula or fork to incorporate the wet ingredients just until combined.
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On a work surface or in the bowl, fold the dough over onto itself using floured hands, a bowl scraper, or the spatula to incorporate any dry floury patches.
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Line a baking sheet with parchment; if you don't have parchment, use an ungreased baking sheet. Sprinkle a bit of flour atop the parchment or pan.
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Transfer the dough to the parchment or pan and divide it in half (about 415g per piece). Use floured hands to pat each piece into a 4" round about 1" thick. Place the pan in the freezer for 15 minutes (this helps firm up the dough for cleaner cuts).
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Using a knife or bench knife that you've run under cold water, slice each circle into 6 wedges. Separate the pieces so that there is at least 1" between them. (Alternatively, place the 12 wedges in a lightly greased Mini Scone Pan; leave 4 spots unfilled. It’s OK if the scone wedges don’t fit perfectly into the wells, as they'll spread out as they bake.) Brush the top of the scones with cream and sprinkle with coarse sugar.
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Place the pan in the oven and immediately reduce the temperature to 375°F. Bake, rotating the pan once halfway through, for 25 to 30 minutes, until the scones are golden brown.
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Remove from the oven. Let the scones cool on/in the pan. While the scones are cooling, prepare the frosting.
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To make the frosting: In a large bowl or the bowl of a stand mixer, beat the cream cheese and butter until light and fluffy. Mix in the confectioners' sugar, then 1 teaspoon of the cream and the salt; beat briefly. Adjust the consistency of the frosting with additional cream or confectioners' sugar, if necessary; it should be nicely spreadable.
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Use a spoon or small offset spatula to spread the frosting over the tops of the scones, or transfer the frosting to a small dish to serve alongside the scones. Serve slightly warm or at room temperature.
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Storage information: Store any leftover scones with cream cheese frosting in an airtight container and keep at room temperature for several days. Freeze unfrosted scones for longer storage; to serve, remove from freezer and let stand at room temperature for 30 minutes, then heat in a 350°F oven until warm.
