Chorizo: In a medium skillet over medium heat, brown the chorizo, breaking it up with a wooden spoon as it cooks, 6–8 minutes (if the chorizo is very lean, add a drizzle of olive oil to the pan). You'll know it's almost done when the cooking sounds "poppy." Add a tablespoon of water and stir, scraping up brown bits from the bottom of the pan. Drain chorizo into a strainer fitted over a bowl to separate solid from rendered fat. Set aside.
Almonds: In the same skillet, over low heat, add 1 tablespoon olive oil. Add almonds and toast until fragrant, 4–6 minutes, stirring occasionally to prevent burning. As they toast, they’ll begin to pop, a signal that they’re done. Drain into the strainer with the chorizo. Set aside.
Garlic and shishitos: Preheat broiler. Wipe out the skillet; add a few tablespoons water to lower the temperature and further deglaze the pan. When the pan is dry, set it over low heat, and add butter and olive oil, followed by slivered garlic (garlic cut lengthwise in thin slivers is ideal for toasting). Toast garlic until golden but not brown, 4–6 minutes. Meanwhile, place shishitos on a rimmed baking sheet and drizzle with 2 tablespoons olive oil and a generous pinch of salt. Broil the peppers until lightly blistered and just starting to soften, shaking the baking sheet occasionally, 3–5 minutes. When garlic is sticky, golden, and caramelized, immediately remove from the heat and drain into the strainer that holds the chorizo and almonds.
Assembly: Remove blistered shishitos from the oven, turn them over, and place back under the broiler 1 more minute. Toss chorizo, almond, and garlic mixture with 1–2 tablespoons of the drained liquid (taste first to make sure it isn’t burnt). Add chopped rosemary, lemon juice, and shishitos. Toss and serve warm.