DontPutAnEditBoxInThat.lua

local DropdownButton;
local FilterEditBox = CreateFrame("EditBox", nil, nil, "InputBoxTemplate");
FilterEditBox:SetAutoFocus(false);  -- Aside; this default has always plagued me.

local DefaultMenuMixin = MenuVariants.GetDefaultMenuMixin();
local CustomMenuMixin = CreateFromMixins(DefaultMenuMixin);

function CustomMenuMixin:Generate()
	DefaultMenuMixin.Generate(self);
	FilterEditBox:ClearAllPoints();
	FilterEditBox:SetParent(self);
	FilterEditBox:SetPoint("TOPLEFT", 8, -8);
	FilterEditBox:SetPoint("TOPRIGHT", -8, -8);
	FilterEditBox:SetHeight(20);

	FilterEditBox:SetScript("OnTextChanged", function(_, userInput)
		if userInput then
			DropdownButton:GenerateMenu();
		end
	end)
end

function CustomMenuMixin:GetInset()
	local l, t, r, b = DefaultMenuMixin.GetInset(self);
	t = t + 30;
	return l, t, r, b;
end

DropdownButton = CreateFrame("DropdownButton", nil, UIParent, "WowStyle1DropdownTemplate");
DropdownButton:SetPoint("CENTER");
DropdownButton:SetDefaultText("rawr");
DropdownButton.menuMixin = CustomMenuMixin;  -- No SetMenuMixin method that I can see?
DropdownButton:SetupMenu(function(_, rootDescription)
	local options = { { "Option 1", 1 }, { "Option 2", 2 }, { "Option 3", 3 } };

	for _, option in ipairs(options) do
		if option[2] >= (FilterEditBox:GetNumber() or 0) then
			rootDescription:CreateButton(option[1], print, option[2]);
		end
	end
end)