Dry the fish skin: 8-10 hours before cooking (or the night before), place the bass fillets skin side up on a plate, uncovered, in the refrigerator. The airflow will dry the skin to a taut, papery texture — the foundation of a truly crispy crust. Do not salt at this stage.
Roast the potatoes: Preheat oven to 425°F. Toss the baby potatoes with the olive oil, salt, pepper, thyme, and smashed garlic. Spread in a single layer on a sheet pan. Roast for 20-25 minutes until deeply golden and fork-tender.
Roast the broccolini: About 10 minutes before the potatoes finish, toss the broccolini with the avocado oil, sliced garlic, red pepper flakes, and a pinch of salt. Spread in a single layer on a second sheet pan and add to the oven alongside the potatoes. Roast for 8-11 minutes until the stems are tender and beginning to color, then move the rack to the top position and broil on high for 2-3 minutes, watching closely, until the floret tips are dark and charred. Squeeze the lemon wedge over the top and keep warm.
Prep the fish: Remove the bass fillets from the fridge 15 minutes before cooking. Score the skin with shallow slits just deep enough to break the membrane, about ⅛ inch deep, spaced ½ inch apart. This prevents curling and maximizes crispiness on thin fillets. Pat the skin dry one final time with a paper towel. Season both sides with the kosher salt right before cooking.
Start the sauce and sear the fish simultaneously: In a small saucepan over medium heat, cook the minced shallot for 3 minutes. Add the white wine and lemon juice and reduce until nearly a syrup, about 2 minutes. Meanwhile, heat a separate stainless steel or cast-iron skillet over high heat until nearly smoking. Add the ghee and swirl to coat. Lay the fillets skin side down. Immediately press each fillet firmly with a spatula for 10 seconds to ensure full skin contact. Do not move them. They will release when ready.
Finish the sauce: Remove the saucepan from heat. Whisk in the cold cubed butter, one cube at a time, until the sauce is glossy and emulsified. Stir in the capers and parsley. Taste and adjust salt. Keep warm on the lowest possible heat or simply off heat. The emulsion will hold for a few minutes.
Finish the fish: After 2 minutes skin side down, flip the fillets, but don't force them to release. Cook the flesh side for just 30-45 seconds. If they took longer to release, just hit them for 20 seconds on the other side. Immediately transfer the fish to a warm plate so they don't overcook in the pan. Place skin side up.
Plate and serve: Place the broccolini in the center of the plate. Place the fish on top of the broccolini. Spoon the beurre blanc alongside or around the fish. You can drizzle a tiny bit over the skin, but not too much or it will go soft. Add the roasted potatoes. Serve at once.