Gloss- Here is a try-
Continuously for centuries after 1350, Ming China is investing in maritime and land-based expansionism. The Chinese end up exploring as far as the Cape before the Portuguese round it, and decide they don't want "Firangi" in the Indian Ocean. They explore to the east and south as well.
Even if the Europeans discover the Americas first, the Ming or a vigorous successor dynasty after a quick transition act fastest on the largest scale to settle the American continents.
By the 1500s, China has a quasi-religious ideology of solving social problems through territorial and demographic expansion, and of bringing wilderness into cultivation and "civilization".
On land, the Chinese empire has a policy of containing nomads by settling temperate forest-regions and bringing them into cultivation, which surrounds Mongols with garrisons and leading to gradual Han Chinese expansion north and westward through the most cultivatable and habitable portions of Siberia. The Chinese meet the Russians at the Urals.
Expanding into many areas where rice cultivation is not possible, the frontier chinese food package involves more wheat, millet and soybeans.
West Europeans still advance in sailing and gunnery technology and their internal markets develop. The Europeans are still the first to claim the Caribbean, Central America, Venezuela, Colombia, southern Mexico and the easternmost coast of North America.
Thus development of European capitalism still benefits from precious metals influx and tropical plantations. Europeans can still slave raid as far south as Angola before clashing with Chinese outposts.
However, from their early and massive starts in California, Oregon, Washington, Peru and Chile, the Chinese demographic steamroller ends up controlling South America south of the Equator or Amazon and North America west of the Appalachians, in addition to the Cape of Africa.
Basically, Chinese preemption of "empty" or less populated temperate lands leaves the Europeans much shorter of land for settlement colonies.
At the same time, China is not an invincible, world absorbing state. At some point during its expansion it is going to have hiccups, and have a change of dynasties. China is supremely uninteresting in getting involved in what the Christians and Muslims do to each other. On the Eurasian mainland, the Chinese don't really give a darn what happens west of the Urals, Caspian and straits of Hormuz. Christian and Muslim military technology also makes any Chinese involvement there more painful and costly.
Buoyed by the Atlantic economy and sugar plantations, European growth picks up in the 1600s. Europe's advantages over the Islamic world really begin to get decisive in the late 1600s. In addition to more capitalism and proto-industry, Europe has more water, lumber, metal and food resources to compete with.
In the 1700s, with expansion to lands of settlement like most of the Americas, Australia, southern Africa and Siberia, the least difficult arena for European imperialism is the Muslim Mediterranean. Russian and Central European "Holy Leagues" bring an early end to the Ottoman Empire, claim the Caucasus and Balkans and in following generations conquer Asia Minor. In the West Mediterranean, Spanish and French and Italian states crush the Barbary pirates earlier and occupy the coastal ports of North Africa. Eventually this spreads to the Levant. By the early 19th century, Russian or European (mostly Catholic, but maybe with some Protestant participation is a Reformation analogue occurs) political rule extends through all former Roman territories and possibly into Iraq, western Persia, all Arabia and Ethiopia.
There are European "colons" in all these occupied areas, and although Muslim resistance is valiant, European demographics and technological edges turn earlier coastal enclaves into a continuous colonized zone.
Europeans may improve their terms of trade in the Sinified areas and may improve their access, but except for small batches of traders, farmers or adventurers, no similar colonization is attempted where Chinese developed the area first.