Set an oven rack to the middle position and preheat oven to 375 °F. Line a large sheet pan with parchment paper. Slice off any discolored or woody portions from brussels sprout stems, making sure to leave enough of the stem intact to hold the leaves together; cut brussels sprouts in half. In a large bowl, mix brussels sprouts, 2 tablespoons olive oil, ½ teaspoon salt and pinch black pepper until evenly coated. Spread brussels sprouts on sheet pan, reserving bowl for later use. Cut lemon in half and place both halves cut–face up in adjacent corners of sheet pan. When oven is preheated, place sheet pan on rack and set timer for 15 minutes.
Place garlic in reserved mixing bowl and toss to coat lightly with excess olive oil. When timer rings, remove brussels sprouts from oven; scatter garlic over brussels sprouts; return sheet pan to oven for another 15 minutes.
Pat salmon fillets dry with paper towel; rub flesh sides evenly with 1 teaspoon olive oil, ¼ teaspoon salt and pinch black pepper. When brussels sprouts have been in the oven for a total of 30 minutes, being careful of hot surfaces, remove sheet pan from oven. Shift brussels sprouts towards side of sheet pan with lemon halves to make room for salmon. Place salmon on sheet pan skin–side down; return sheet pan to oven; roast until salmon is opaque pink through thickest part of the fillet and flakes apart easily with a fork, 10-15 minutes.
Meanwhile, fill a large pot with water and ¼ cup salt; bring to a boil over high heat. Add pasta to boiling water; cook, stirring occasionally to avoid clumping, until al dente, about 10 minutes or according to product’s suggested time. Pasta should be firm to the bite, but with no pale or starchy center. Drain pasta, reserving pot for later use; rinse lightly to stop cooking; transfer pasta to reserved mixing bowl. Toss pasta with 1 tablespoon olive oil and set aside.
Transfer salmon, garlic, and lemon to cutting board. When cool enough to handle, peel garlic; remove skin from salmon and shred salmon into 2-3 inch pieces. In reserved pasta pot, heat remaining 1 tablespoon olive oil over medium heat. Add garlic; with edge of spatula mix and mash garlic until mostly smooth and sizzling, about 1 minute. If garlic begins to burn or stick to bottom of pot, reduce heat to medium–low. In fine mesh strainer held over the garlic mixture, squeeze lemon halves; press juice and pulp through strainer with back of spoon. Add honey, thyme leaves and ¼ teaspoon salt; cook, stirring, until fragrant, about 1 minute. Reduce heat to medium–low; add pasta and brussels sprouts; gently stir to coat with garlic mixture. Adjust seasoning with salt and black pepper to taste. Remove pasta from heat; gently fold in salmon and taleggio; serve.