For the cornish hens: Season the hen halves with salt and refrigerate, uncovered, overnight so the skin can dry out.
When the meat is ready, preheat the oven to 400 degrees F. Line a sheet pan with a rack and set aside.
Stir together 2 tablespoons of the olive oil, the garlic, rosemary, lemon zest and salt to taste, then set aside. Add the remaining 2 tablespoons olive oil to a large saute pan and heat over high heat. Working in batches, place 2 hen halves in the pan skin-side down and cover with the foil-lined brick. Reduce the heat to medium and cook until the skin is golden brown and crispy, 4 to 5 minutes. Remove the brick, flip the pieces and cook 3 to 4 minutes more. Transfer to the prepared sheet pan skin-side up. Repeat with the remaining 2 hen halves, reserving the saute pan. Brush the hens with the oil, garlic and rosemary mixture and bake until the internal temperature reaches 165 degrees F, 8 to 10 minutes. Remove from the oven and keep warm.
While the hens are baking, heat the reserved saute pan over medium-high heat, add the shallots and saute until translucent, 5 minutes. Add the mushrooms and cook 2 to 3 minutes. Deglaze the pan with the wine, then add the sage. Cook until the wine is reduced, 2 to 3 minutes more. Add the stock and cook until reduced by half, 5 minutes. Finish the sauce with the butter and lemon juice and keep warm.
For the green beans: Set up a large pot of well-salted boiling water. Set up a large bowl of well-salted ice water. Blanch the green beans until bright green and tender, but still crisp, 1 minute. Remove from the boiling water and plunge them immediately into the ice bath. Once the beans are cool, remove them and pat dry.
Combine the olive oil, garlic, and red pepper flakes in a medium saute pan. Turn the heat to medium and gently cook until the garlic is golden brown, but not burnt, 3 to 5 minutes. Discard the garlic, then add the green beans and toss to coat in the garlic oil. Add the almonds and toss to combine.
Serve the cornish hens with the sauce and green beans.