Preheat oven to 325°F. Grease a 10–12 cup Bundt pan thoroughly, including every ridge.
Melt the butter in a small saucepan over medium heat, swirling occasionally, until the milk solids turn golden-brown and smell nutty, about 5–7 minutes. Pour into a heatproof bowl and cool to room temperature, about 20 minutes.
Whisk the agave nectar and sugar into the cooled browned butter. Add the eggs one at a time, whisking well after each addition, until glossy.
Whisk in the sour cream, orange zest, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Fold into the wet batter in two additions, mixing just until no flour streaks remain.
Pour batter into the prepared Bundt pan and smooth the top. Bake for 40–45 minutes, until a toothpick inserted near the center comes out with a few moist crumbs and the top springs back when pressed gently.
Cool in the pan for 15 minutes, then invert onto a wire rack to cool almost completely, about 45 minutes.
While the cake cools, whisk the agave nectar, butter, and orange juice in a small saucepan over low heat until glossy and slightly thickened, about 2 minutes.
Once the cake is barely warm to the touch, pour the glaze evenly over the top, letting it drip down the sides. Finish with a pinch of flaky sea salt. Slice and serve.