Heat the oven to 325°F. Lightly butter a 9-inch springform pan and line the base with parchment. Set the sour cream and eggs out to lose their chill.
Spread the chopped pecans on a small sheet pan and toast in the warming oven for 5–6 minutes, just until fragrant; cool briefly. In a bowl, mix the brown sugar, cinnamon, cardamom, salt, and toasted pecans. Set the ripple mixture aside.
Whisk together the flour, baking powder, and 1/2 teaspoon salt in a medium bowl to combine and aerate.
In a large mixing bowl, beat the butter and granulated sugar on medium-high until very light and fluffy, 2–3 minutes. Beat in the orange zest and vanilla. Add the eggs one at a time, mixing well and scraping down the bowl after each addition.
On low speed, add the dry ingredients in three additions, alternating with the sour cream in two additions (dry–sour cream–dry–sour cream–dry). Mix just until the last streak of flour disappears. Let the batter rest for 5 minutes to relax and thicken slightly.
Spoon about two-thirds of the batter into the pan and smooth the top. Sprinkle half of the cinnamon-pecan mixture evenly over the batter.
Dollop the remaining batter over the sugared nuts, then use a thin knife or skewer to make a lazy figure-eight pass through the batter to create a gentle ripple. Sprinkle the remaining cinnamon-pecan mixture over the surface.
Bake until the cake is golden and a toothpick inserted near the center comes out clean or with a few moist crumbs, 50–58 minutes, rotating the pan once after 35 minutes. If the top browns too fast, tent loosely with foil for the final 10 minutes.
Cool on a rack for 15 minutes, then release the springform ring. Let cool at least 45 minutes more before slicing for the cleanest cuts.