How to rotate a group of floating, anchored bricks, on a center axis?

You can accomplish this with welds by unanchoring all them, welding them together, and welding some other anchored object to one of the parts (e.g., the baseplate).

Instead, if you want to use CFrame, you can fairly easily do this using cframe:toObjectSpace(cframe) and cframe:toWorldSpace(cframe):

-- Twists all parts in `model` angle `angle` (in radians) about the Y axis
function twist(model, angle)
    local origin = CFrame.new();
    local out = origin * CFrame.Angles(0, angle, 0);
    for _, part in pairs(model:GetChildren()) do
        if part:IsA("BasePart") then
            part.CFrame = out:toWorldSpace(
                origin:toObjectSpace(part.CFrame)
            );
        end
    end
end

For example, to make it spin, you could use

while true do
    wait();
    twist(workspace.Model, 0.1)
end