Actually, looking at this page source, and I may be wrong, but it seems that this is not a standard Vaadin cell box

An alternative workaround based on your discussion with @defaultlocale might group a button with combos like

or that:

In any case, you can customize the code below to your liking, and you can also check sampler sources for more examples.
public class ComboWithIcon extends CssLayout { public ComboWithIcon() {
Edit later
According to the above and your last board, you can also delete your borders, group them in a layout and add a layout to the panel for a general border effect (perhaps a more elegant solution for getting a border, but I did not find the default styles, and I have no more time to investigate, therefore suggestions are welcome):
public class ComboWithIcon extends Panel { public ComboWithIcon() {
with a slight theme setting to avoid focusing on the button
.v-button-no-focus:after { content: none; }
and get:

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