Heat a large skillet over medium-high heat and add olive oil. Add shallots and garlic and saute for 1-2 minutes, until fragrant. Add in brussels spouts (I like to start with mine cut side down), salt and pepper, and cook for 8-10 minutes, tossing brussels every so often, until browned. While brussels are cooking, heat a small saucepan over medium heat and add butter. Whisk fairly continuously until butter begins to get golden in color and brown flecks appear. Remove from heat immediately.