In a glass jar with a tight-fitting lid, combine dressing ingredients, shake until emulsified and set aside.
Halve the fennel bulb and remove the core. As thinly as possible, slice the fennel lengthwise. Use a mandolin, extra-thin blade on your food processor, vegetable peeler or a knife. Place fennel in a large bowl.
With a sharp knife, remove the peel and pith from the blood oranges and segment the slices. See my blogpost “How to Segment Citrus” for a visual.*
Arrange the fennel across a big platter and toss with enough dressing to moisten lightly.
Tuck the citrus segments and avocado slices into the fennel and scatter the cheese. Drizzle remaining dressing or only as much as is needed.
Garnish with fennel fronds, if desired. Sprinkle with flaky sea salt.