2 large fennel bulbs
3/4 pound shallots
1/4 cup olive oil, divided
1 cup orange juice
1/2 teaspoon sea salt
2 teaspoons minced flat-leaf parsley
1 teaspoon orange zest, grated with a coarse microplane
Trim the tops off of the bulbs of fennel and slice away a small amount of the root end, just to remove any discolored surface. Peel away the outermost layer of the bulbs if they are brown or bruised. Cut the bulbs in half from root to stem, then slice the halves into wedges, being careful to keep some of the root end attached to each slice. (See step-by-step instructions for How to Cut Fennel.)
Slice off the top and bottom of each shallot, making sure not to slice off the whole root end. Use a paring knife to peel away the outer skins. Larger shallots tend to grow into two separate segments — pull these apart, then halve the smaller segments and quarter the larger ones, slicing from root to stem end, creating wedges of shallots.
Heat one tablespoon of olive oil in a 12-inch skillet over medium heat. When the oil begins to shimmer in the pan, add a single layer of fennel slices and sear until lightly browned, about 2 minutes. Use tongs to gently flip the fennel and brown on the other side for another 1 to 2 minutes, then transfer to a plate. Repeat with the remaining fennel and shallots, adding a tablespoon of oil to the pan each time. Transfer all vegetables to the plate as they are seared.
Set the empty skillet used to sear the vegetables back over medium heat and add the orange juice. Use a spatula to scrape any browned bits off of the bottom of the pan. When the orange juice begins to simmer, add the seared shallots and fennel back to the pan. Sprinkle with salt and stir to coat with orange juice. Cover the skillet and lower the heat slightly to medium-low. Cook until the vegetables are tender and orange juice has reduced to a glaze, about 15 minutes.
Transfer the braised vegetables to a serving platter, using a spatula to scrape all of the glaze out of the skillet. Sprinkle with parsley and orange zest and serve.