Bnei Yisrael crown Hashem as King on Rosh Hashanah

בענין אמרו לפני מלכיות שתמליכוני עליכם.

Concerning the teaching, "Recite before Me Malchuyos (verses of kingship), so that you may crown Me as King over you" (Rosh Hashanah 16a, 34b).

The Sefas Emes addresses Hashem's request that on Rosh Hashanah we recite the Malchuyos verses in order to coronate Him as our King.

עפ"י מ"ש ואתם תהיו לי ממלכת כהנים פרש"י שרים כו'.

Based on what is written, "And you shall be to Me a kingdom of priests" (Shemos 19:6) — Rashi explains "kohanim" here to mean nobles/ministers (sarim).

He builds on Rashi's reading that "a kingdom of kohanim" means that Bnei Yisrael are like sarim, the nobles and ministers who attend upon a king.

כמו שיש שרים שממליכים המלך אעפ"י שהמלך מושל עליהם.

Just as there are ministers who coronate the king, even though the king rules over them.

In a kingdom, it is the nobles who proclaim and crown the king, even though he in fact reigns over them — their acceptance gives his kingship its public expression.

כמו כן כביכול רצה השי"ת שבנ"י ימליכו אותו וכפי קבלת מלכות שמים שהמה מקבלים כך מתגלה כבוד מלכותו ית' בעולם.

So too, as it were, Hashem desired that Bnei Yisrael crown Him, and according to the degree of malchus shomayim (the sovereignty of Heaven) that they accept, so is the glory of His kingship revealed in the world.

Hashem chose Bnei Yisrael as His "ministers" to coronate Him. The measure in which they accept the yoke of malchus shomayim determines how much of His royal glory becomes revealed throughout creation.

והכל בכח קבלת התורה זכו בנ"י לזה כמ"ש אם שמוע תשמעו בקולי כו'.

And all of this — Bnei Yisrael merited it through the power of Kabbalas HaTorah, as it is written, "If you will surely hearken to My voice…" (Shemos 19:5).

Bnei Yisrael earned this exalted role of crowning Hashem by accepting the Torah, which the verse introduces with the condition of hearkening to His voice.

ונרמז ג"כ מצות שמיעת קול שופר שהיא רמז לקבלת התורה ועי"ז תהיו לי ממלכת כהנים הוא בר"ה זמן המלוכה.

And this is also alluded to in the mitzvah of hearing the sound of the shofar, which is a hint to Kabbalas HaTorah; and through this, "you shall be to Me a kingdom of priests" is realized on Rosh Hashanah, the time of the coronation.

The mitzvah to hear the shofar echoes the "voice" of Sinai, recalling Kabbalas HaTorah. Through hearkening to the shofar, Bnei Yisrael fulfill their role as the "kingdom of priests" who crown Hashem on Rosh Hashanah, the day of coronation.

וגוי קדוש הוא ביום הכפורים שנמשלו בנ"י למלאכים כמ"ש חז"ל:

And "a holy nation" (Shemos 19:6) is realized on Yom Kippur, when Bnei Yisrael are compared to angels, as Chazal taught.

The verse's two crowns are fulfilled across the Yamim Noraim: "a kingdom of priests" on Rosh Hashanah, when Bnei Yisrael crown Hashem, and "a holy nation" on Yom Kippur, when they rise to the angelic level of purity that Chazal describe.

Summary: The Sefas Emes explains that Hashem wants Bnei Yisrael to crown Him with the Malchuyos verses because, like the ministers who coronate a king, the measure of malchus shomayim they accept determines how much of His royal glory is revealed in the world. This role was earned through Kabbalas HaTorah and is re-enacted by hearing the shofar. Thus "a kingdom of priests" is fulfilled on Rosh Hashanah, the time of coronation, and "a holy nation" on Yom Kippur, when Bnei Yisrael become like angels.